Method and apparatus for encoding and mapping magnetic disk sector addresses

Claim 3

The method of claim 1 wherein said encoding step further includes encoding said n-bit address code word using a (p,n) distance E linear code over Galois Field GF(2) to produce p-n redundancy symbols and appending said redundancy symbols to said n-bit address code word to form a p-bit address code word such that the p-bit address code word differs from any other p-bit address codeword by at least E.[.-1/2.]. bits .Iadd.and differs from any other p-bit address code word in a 2 k neighborhood of said sector in at least D-1 bits, where D-1.E. .Iaddend. .[.

Claim 4

The method of claim 2 wherein said encoding step further includes encoding said n-symbol address code word using a (p,n) distance E linear code over Galois Field GF(2 m ) to produce p-n redundancy symbols and appending said redundancy symbols to said n-symbol address code word to form a p-symbol address code word such that the p-symbol address code word differs from any other p-symbol address codeword by at least E-1/2 symbols..].

Claim 5

The method of claim 1 wherein said comparison step further includes adding modulo 2 said address code words and said specified address code words.

Claim 8

representing said n-k higher order symbol segment in binary Gray code; 4. adding modulo 2 said Gray coded segment to the n-k higher order symbols of said n-symbol code word to produce an n-symbol address code word; B. recording said address code words in the sectors during the formatting of the disk; C. reading said address code word from the sector rotating under the head.Iadd., said sector being within a 2 mk neighborhood of the sector to be located.Iaddend.; D. encoding the specified address of the sector to be located in the same manner of step A to produce a specified address code word; E. comparing said sector address code word read from a disk sector with said specified address code word; F. (1) if the comparison results in a number of symbols which differ between said address code word and said specified address code word that is less than a predetermined number, identifying the sector as the correct sector; or (2) if the comparison results in a number of symbols which differ that is greater than said predetermined number, not identifying the sector as the correct sector.

Claim 9

representing said n-k higher order symbol segment in binary Gray code; 4. adding modulo 2 said Gray coded segment to the n-k higher order symbols of said n-symbol code word to produce an n-symbol address code word; B. recording said address code words in the sectors during the formatting of the disk; C. reading said address code word from the sector rotating under the head.Iadd., said sector being within a 2 mk neighborhood of the sector to be located.Iaddend.; D. encoding the specified address of the sector to be located in the same manner of step A to produce a specified address code word; E. comparing said sector address code word read from a disk sector with said specified address code word; F. (1) if the comparison results in a number of symbols which differ between said address code word and said specified address code word that is less than a predetermined number, identifying the sector as the correct sector; or (2) if the comparison results in a number of symbols which differ that is greater than said predetermined number, not identifying the sector as the correct sector.

Claim 12

means for separating the sector address containing n bits into two segments, a k lower order bit segment and an n-k higher order bit segment; 2. means for using a distance D linear (n,k) code over Galois Field GF(2) to encode said k-bit segment into an n-bit code word containing n-k redundancy symbols and the k address bits .[.such that any two encoded addresses differ by at least D-1/2 bits; .]. .Iadd.such that any two n-bit code words corresponding to sectors within a 2 k neighborhood differ in at least D bits.Iaddend. bits, 3. means for representing said n-k .[.redundancy symbol.]. .Iadd.higher order bit .Iaddend.segment in Gray code; 4. means for adding said Gray coded segment to the n-k higher order bits of said n-bit code word to produce an n-bit address code word; B. means for recording said address code words in the sectors during the formatting of the disk; C. means for encoding the specified address of the sector to be located in the same manner of step A to produce a specified address code word; D. means for comparing said address code word read from a disk sector .Iadd.which is within a 2 k neighborhood of the sector to be located .Iaddend.with said specified address code word; E. (1) if the comparison results in a number of bits which differ between said address code word and said specified address code word that is less than a predetermined number, means for identifying the sector as the correct sector; or (2) if the comparison results in a number of bits which differ that is greater than said predetermined number, not identifying the sector as the correct sector.

Claim 13

means for separating the sector address containing n bits into two segments, a k lower order bit segment and an n-k higher order bit segment; 2. means for using a distance D linear (n,k) code over Galois Field GF(2) to encode said k-bit segment into an n-bit code word containing n-k redundancy symbols and the k address bits .[.such that any two encoded addresses differ by at least D-1/2 bits; .]. .Iadd.such that any two n-bit code words corresponding to sectors within a 2 k neighborhood differ in at least D bits.Iaddend. bits, 3. means for representing said n-k .[.redundancy symbol.]. .Iadd.higher order bit .Iaddend.segment in Gray code; 4. means for adding said Gray coded segment to the n-k higher order bits of said n-bit code word to produce an n-bit address code word; B. means for recording said address code words in the sectors during the formatting of the disk; C. means for encoding the specified address of the sector to be located in the same manner of step A to produce a specified address code word; D. means for comparing said address code word read from a disk sector .Iadd.which is within a 2 k neighborhood of the sector to be located .Iaddend.with said specified address code word; E. (1) if the comparison results in a number of bits which differ between said address code word and said specified address code word that is less than a predetermined number, means for identifying the sector as the correct sector; or (2) if the comparison results in a number of bits which differ that is greater than said predetermined number, not identifying the sector as the correct sector.

Claim 14

The apparatus of claim 6 wherein said encoding means further comprises means for encoding said n-bit address code word using a (p,n) distance E linear code over Galois Field GF(2) to produce p-n redundancy symbols and appending said redundancy symbols to said n-bit address code word to form a p-bit address code word such that the p-bit address code word differs from any other p-bit address codeword .[.by.]. .Iadd.in .Iaddend.at least E .[.-1/2.]. bits .Iadd.and differs from any other p-bit address code word in a 2 k neighborhood of said sector by at least D-1 bits, where D-1.E. .Iaddend.

Claim 15

The apparatus of claim 6 wherein said comparison means further includes means for .[.step further includes.]. adding modulo 2 said address code words and said specified address code words.

Claim 18

The apparatus of claim 9 wherein said encoding means further comprises means for encoding said n-symbol address code word using a (p,n) distance E linear code over Galois Field GF(2 m ) to produce p-n redundancy symbols and appending said redundancy symbols to said address code word to form a p-symbol address code word such that the p-symbol address code word differs from any other p-symbol address codeword by at least E symbols .Iadd.and differs from any other p-symbol address code word in a 2 mk neighborhood of said sector by at least D-1 symbols, where D-1>E. .Iaddend.

Claim 19

The apparatus of claim 9 wherein said comparison means further includes means for adding modulo 2 said address code words and said specified address code words.

Claim 22

The method of claim 12 wherein said encoding step further includes encoding said n-bit address code word using a distance E linear (p,n) code over Galois Field GF(2) to produce p-n redundancy symbols and appending said redundancy symbols to said n-bit address code word to form a p-bit address code word such that the p-bit address code word differs from any other p-bit address codeword by at least E .[.-1/2.]. bits. .[.14. The method of claim 12 wherein said encoding step further includes encoding said n-symbol address codes word using a distance E linear (p,n) code over Galois Field GF(2) to produce p-n redundancy symbols and appending said redundancy symbols to said n-symbol address code word such that the p-symbol address code word differs from any other p-symbol address

Claim 23

codeword by at least E-1/2 symbols..]. 15. An apparatus for encoding magnetic disk data sector addresses comprising: A. means for encoding the addresses of the sectors to produce address code words comprising: 1. means for separating the sector address containing n bits into two segments, a k lower order bit segment and an n-k higher order bit segment; 2. means for using a distance D linear (n,k) code over Galois Field GF(2) to encode said k-bit segment into an n-bit code word containing n-k redundancy symbols and the k address bits .[.such that any two encoded addresses differ by at least D-1/2 bits.]. .Iadd.such that any two n-bit code words corresponding to sectors within a 2 k neighborhood differ in at least D bits; .Iaddend. 3. means for representing said n-k .[.redundancy symbol.]. .Iadd.higher order bit .Iaddend.segment in Gray code; 4. means for adding said Gray coded segment to the n-k higher order bits of said n-bit code word to produce an n-bit address code word; and B. means for recording said address code words in the sectors during the

Claim 24

codeword by at least E-1/2 symbols..]. 15. An apparatus for encoding magnetic disk data sector addresses comprising: A. means for encoding the addresses of the sectors to produce address code words comprising: 1. means for separating the sector address containing n bits into two segments, a k lower order bit segment and an n-k higher order bit segment; 2. means for using a distance D linear (n,k) code over Galois Field GF(2) to encode said k-bit segment into an n-bit code word containing n-k redundancy symbols and the k address bits .[.such that any two encoded addresses differ by at least D-1/2 bits.]. .Iadd.such that any two n-bit code words corresponding to sectors within a 2 k neighborhood differ in at least D bits; .Iaddend. 3. means for representing said n-k .[.redundancy symbol.]. .Iadd.higher order bit .Iaddend.segment in Gray code; 4. means for adding said Gray coded segment to the n-k higher order bits of said n-bit code word to produce an n-bit address code word; and B. means for recording said address code words in the sectors during the

Claim 25

formatting of the disk. 16. The apparatus of claim 15 wherein said encoding means further comprises means for encoding said n-bit address code word using a distance E linear (p,n) code over Galois Field GF(s) to produce p-n redundancy symbols and appending said redundancy symbols to said address code word to form a p-bit address code word such that the p-bit address code word differs from any other p-bit address codeword by

Claim 26

at least E .[.-1/2.]. bits. 17. An apparatus for locating a sector on a magnetic disk comprising: A. means for reading an address code word from the sector rotating under the head; B. means for encoding the specified address of the sector to be located to produce an address code word comprising: 1. means for separating the sector address containing n bits into two segments, a k lower order bit segment and an n-k higher order bit segment;

Claim 27

at least E .[.-1/2.]. bits. 17. An apparatus for locating a sector on a magnetic disk comprising: A. means for reading an address code word from the sector rotating under the head; B. means for encoding the specified address of the sector to be located to produce an address code word comprising: 1. means for separating the sector address containing n bits into two segments, a k lower order bit segment and an n-k higher order bit segment;

Claim 28

means for using a distance D linear (n,k) code over Galois Field GF(2) to encode said k-bit segment into an n-bit code word containing n-k redundancy symbols and the k address bits .[.such that any two encoded addresses differ by at least D-1/2 bits.]. .Iadd.such that any two n-bit code words corresponding to sectors within a 2 k neighborhood differ in at least D bits; .Iaddend. 3. means for representing said n-k .[.redundancy symbol.]. .Iadd.higher order bit .Iaddend.segment in Gray code; 4. means for adding said Gray coded segment to the n-k higher order bits of said n-bit code word to produce an n-bit address code word; C. means for comparing said specified address code word with the sector address code word read from a disk sector, .Iadd.said disk sector being within a 2 k neighborhood of the sector be to located; .Iaddend. D. (1) if the comparison results in a number of bits which differ between said address code word and said specified address code word that is less than a predetermined number, identifying the sector as the correct sector; or (2) if the comparison results in a number of bits which differ that is greater than said predetermined number, not identifying the sector as the

Claim 29

means for using a distance D linear (n,k) code over Galois Field GF(2) to encode said k-bit segment into an n-bit code word containing n-k redundancy symbols and the k address bits .[.such that any two encoded addresses differ by at least D-1/2 bits.]. .Iadd.such that any two n-bit code words corresponding to sectors within a 2 k neighborhood differ in at least D bits; .Iaddend. 3. means for representing said n-k .[.redundancy symbol.]. .Iadd.higher order bit .Iaddend.segment in Gray code; 4. means for adding said Gray coded segment to the n-k higher order bits of said n-bit code word to produce an n-bit address code word; C. means for comparing said specified address code word with the sector address code word read from a disk sector, .Iadd.said disk sector being within a 2 k neighborhood of the sector be to located; .Iaddend. D. (1) if the comparison results in a number of bits which differ between said address code word and said specified address code word that is less than a predetermined number, identifying the sector as the correct sector; or (2) if the comparison results in a number of bits which differ that is greater than said predetermined number, not identifying the sector as the

Claim 30

correct sector. 18. The apparatus of claim 17 wherein said comparison means further includes means for adding modulo 2 said address code words

Claim 31

and said specified address code words. 19. The apparatus of claim 17 wherein said encoding means further comprises means for encoding said n-bit address code word using a distance E linear (p,n) code over Galois Field GF(2) to produce p-n redundancy symbols and appending said redundancy symbols to said n-bit address code word to form a p-bit address code word such that the p-bit address code word differs from any other p-bit address codeword by at least E bits .Iadd.and differs from any other p-bit address code word in a 2 k neighborhood of said sector by at

Claim 32

least D-1 bits, where D-1>E. .Iaddend. 20. A method of locating magnetic disk data sectors comprising the steps of: A. reading the address code word recorded in the sector rotating under the head; B. encoding the specified address of the sector to be located by: 1. separating the specified address containing n bits into two segments, a segment containing k lower order bits and a segment containing n-k higher order bits; 2. using a distance D linear (n,k) code over Galois Field GF(2) to encode said k-bit segment into an n-bit code word containing n-k redundancy symbols and the k address bits; 3. representing said n-k .[.redundancy symbol.]. .Iadd.higher order bit .Iaddend.segment in Gray code; 4. adding said Gray coded segment to the n-k higher order bits of said n-bit code word to produce an n-bit address code word; C. comparing said specified address code word with the address code word read from a disk sector.Iadd., said sector being within a 2 k neighborhood of the sector to be located; .Iaddend.and D. (1) if the comparison results in a number of bits which differ between said address code word and said specified address code word that is less than a predetermined number, identifying the sector as the correct sector; or (2) if the comparison results in a number of bits which differ that is greater than said predetermined number, not identifying the sector as the

Claim 33

least D-1 bits, where D-1>E. .Iaddend. 20. A method of locating magnetic disk data sectors comprising the steps of: A. reading the address code word recorded in the sector rotating under the head; B. encoding the specified address of the sector to be located by: 1. separating the specified address containing n bits into two segments, a segment containing k lower order bits and a segment containing n-k higher order bits; 2. using a distance D linear (n,k) code over Galois Field GF(2) to encode said k-bit segment into an n-bit code word containing n-k redundancy symbols and the k address bits; 3. representing said n-k .[.redundancy symbol.]. .Iadd.higher order bit .Iaddend.segment in Gray code; 4. adding said Gray coded segment to the n-k higher order bits of said n-bit code word to produce an n-bit address code word; C. comparing said specified address code word with the address code word read from a disk sector.Iadd., said sector being within a 2 k neighborhood of the sector to be located; .Iaddend.and D. (1) if the comparison results in a number of bits which differ between said address code word and said specified address code word that is less than a predetermined number, identifying the sector as the correct sector; or (2) if the comparison results in a number of bits which differ that is greater than said predetermined number, not identifying the sector as the

Claim 34

correct sector. 21. The method of claim 20 wherein said encoding step further comprises encoding said n-bit address code word using a distance E linear (p,n) code over Galois Field GF(2) to produce p-n redundancy symbols and appending said redundancy symbols to said n-bit address code word to form a p-bit address code word such that the p-bit address code word differs from any other p-bit address codeword by at least E bits .Iadd.and differs from any other p-bit address code word in a 2 k neighborhood of said sector by at least D-1 bits, where D-1>E. .Iaddend. .[.22. The apparatus of claim 20 wherein said encoding means further comprises means for encoding sand n-symbol address code word using a distance E linear (p,n) code cover Galois Field GF(2 m ) to produce p-n redundancy symbols and appending said redundancy symbols to said n-symbol address code word to form a p-symbol address code word such that the p-symbol address code word differs from any other p-symbol address

Claim 35

codeword by at least E-1/2 symbols..]. 23. The apparatus of claim 20 wherein said comparison means further includes means for adding modulo 2 said address code words and said specified address code words. .[.24. The apparatus of claim 20 wherein said comparison means further includes means for adding modulo 2 said address code words and said specified address

Claim 36

code words..]. 25. An apparatus for encoding magnetic disk sector addresses comprising: A. means for encoding the addresses of the sectors to produce address code words by: 1. separating the sector address containing n bits into two segments, a segment containing k lower order bits and a segment containing n-k higher order bits; 2. means for using a distance D linear code over Galois Field GF(2 m ) to encode said k-.[.bit.]. .Iadd.symbol .Iaddend.segment into an n-.[.bit.]. .Iadd.symbol .Iaddend.code word containing n-k redundancy symbols and the k address .[.bits.]. .Iadd.symbols.Iaddend.; 3. means for representing said n-k higher order .[.bit.]. .Iadd.symbol .Iaddend.segment in Gray code; 4. means for adding said Gray coded segment to the n-k higher order .[.bits.]. .Iadd.symbols .Iaddend.of said n-.[.bit.]. .Iadd.symbol .Iaddend.code word to produce an n-.[.bit.]. .Iadd.symbol .Iaddend.address code word; and B. means for recording said address code words in the sectors during the

Claim 37

code words..]. 25. An apparatus for encoding magnetic disk sector addresses comprising: A. means for encoding the addresses of the sectors to produce address code words by: 1. separating the sector address containing n bits into two segments, a segment containing k lower order bits and a segment containing n-k higher order bits; 2. means for using a distance D linear code over Galois Field GF(2 m ) to encode said k-.[.bit.]. .Iadd.symbol .Iaddend.segment into an n-.[.bit.]. .Iadd.symbol .Iaddend.code word containing n-k redundancy symbols and the k address .[.bits.]. .Iadd.symbols.Iaddend.; 3. means for representing said n-k higher order .[.bit.]. .Iadd.symbol .Iaddend.segment in Gray code; 4. means for adding said Gray coded segment to the n-k higher order .[.bits.]. .Iadd.symbols .Iaddend.of said n-.[.bit.]. .Iadd.symbol .Iaddend.code word to produce an n-.[.bit.]. .Iadd.symbol .Iaddend.address code word; and B. means for recording said address code words in the sectors during the

Claim 38

formatting of the disk. 26. The apparatus of claim 25 wherein said encoding means further comprises means for encoding said n-.[.bit.]. .Iadd.symbol .Iaddend.address code word using a distance E linear (p,n) code over Galois Field GF(.Iadd.2.Iaddend. m ) to produce p-n redundancy symbols and appending said redundancy symbols to said .[.n-bit.]. .Iadd.n-symbols .Iaddend.address code word to form a p-.[.bit.]. .Iadd.symbol .Iaddend.address code word such that the p-.[.bit.]. .Iadd.symbol .Iaddend.address code word differs from any other p-bit address codeword in at least E .[.bits.]. .Iadd.symbols and differs from any other p-symbol address code word in a 2 mk neighborhood of

Claim 39

said sector by at least D-1 symbols, where D-1>E. .Iaddend. 27. An apparatus for locating sectors on a magnetic disk comprising: A. means for reading said address code word from the sector rotating under the head; B. encoding means for encoding the specified address of the sector to be located, said encoding means including: 1. means for separating the sector address containing n .[.m-bits.]. .Iadd.m-bit .Iaddend.symbols into two segments, a segment containing k lower order symbols and a segment containing n-k higher order symbols; 2. means for using a distance D linear (n,k) code over Galois Field GF(2 m ) to encode said k-symbol segment into an n-symbol code word containing n-k redundancy symbols and the k-address symbols .[.such that any two encoded addresses differ by at least D-1/2 symbols.]. .Iadd.such that any two n-symbol code words corresponding to sectors within a 2 mk neighborhood differ in at least D symbols; .Iaddend. 3. means for representing said n-k .[.redundancy.]. .Iadd.higher order .Iaddend.symbol segment in Gray code; 4. means for adding said Gray coded segment to the n-k higher order symbols of said n-symbol code word to produce an n-symbol address code word; C. means for comparing said sector address code word read from a disk sector .Iadd.which is within a 2 mk neighborhood of said sector to be located .Iaddend.with said specified address code word; D. (1) if the comparison results in a number of symbols which differ between said address code word and said specified address code word that is less than a predetermined number, means for identifying the sector as the correct sector; or (2) if the comparison results in a number of symbols which differ that is greater than said predetermined number, not identifying the sector as the

Claim 40

said sector by at least D-1 symbols, where D-1>E. .Iaddend. 27. An apparatus for locating sectors on a magnetic disk comprising: A. means for reading said address code word from the sector rotating under the head; B. encoding means for encoding the specified address of the sector to be located, said encoding means including: 1. means for separating the sector address containing n .[.m-bits.]. .Iadd.m-bit .Iaddend.symbols into two segments, a segment containing k lower order symbols and a segment containing n-k higher order symbols; 2. means for using a distance D linear (n,k) code over Galois Field GF(2 m ) to encode said k-symbol segment into an n-symbol code word containing n-k redundancy symbols and the k-address symbols .[.such that any two encoded addresses differ by at least D-1/2 symbols.]. .Iadd.such that any two n-symbol code words corresponding to sectors within a 2 mk neighborhood differ in at least D symbols; .Iaddend. 3. means for representing said n-k .[.redundancy.]. .Iadd.higher order .Iaddend.symbol segment in Gray code; 4. means for adding said Gray coded segment to the n-k higher order symbols of said n-symbol code word to produce an n-symbol address code word; C. means for comparing said sector address code word read from a disk sector .Iadd.which is within a 2 mk neighborhood of said sector to be located .Iaddend.with said specified address code word; D. (1) if the comparison results in a number of symbols which differ between said address code word and said specified address code word that is less than a predetermined number, means for identifying the sector as the correct sector; or (2) if the comparison results in a number of symbols which differ that is greater than said predetermined number, not identifying the sector as the

Claim 41

correct sector. 28. The apparatus of claim 27 wherein said comparison means further includes means for adding modulo 2 said address code words

Claim 42

and said specified address code words. 29. The apparatus of claim 27 wherein said encoding .[.means.]. .Iadd.step .Iaddend.further comprises means for encoding said .[.n-symbols.]. .Iadd.n-symbol .Iaddend.address code word using a distance E linear (p,n) code over Galois Field GF(2 m ) to produce p-n redundancy symbols and appending said redundancy symbols to said .[.n-symbols.]. .Iadd.n-symbol .Iaddend.address code word to form a .[.p-symbols.]. .Iadd.p-symbol .Iaddend.address code word such that the .[.p-symbols.]. symbols .Iadd.p-symbol .Iaddend.address code word differs from any other .[.p-symbols.]. .Iadd.p-symbol .Iaddend.address codeword by at least E.[.-1/2.]. symbols .Iadd.and differs from any other p-symbol address code word in a 2 mk neighborhood of said sector by at least D-1 symbols, where D-1 E.

Claim 43

.Iaddend. 30. A method for locating data sectors on a magnetic disk during sector seeking operations comprising the steps of: A. encoding the addresses of the sectors to produce address code words comprising:

Claim 44

.Iaddend. 30. A method for locating data sectors on a magnetic disk during sector seeking operations comprising the steps of: A. encoding the addresses of the sectors to produce address code words comprising:

Claim 45

separating the sector address containing n m-bit symbols into two segments, a k lower order symbol segment and an n-k higher order symbol segment, 2. using a distance D linear (n,k) code over Galois Field GF(2 m ) to encode said k-symbol segment into an n-symbol code word containing n-k redundancy symbols and the k address symbols .[.such that any two encoded addresses differ by at least D-1/2 symbols.]. .Iadd.such that any two n-symbol code words corresponding to sectors within a 2 mk neighborhood differ in at least D symbols.Iaddend., 3. representing said n-k .[.redundancy.]. .Iadd.higher order .Iaddend.symbol segment in binary Gray code, 4. adding modulo 2 said Gray coded segment to the n-k higher order symbols of said n-symbol code word to produce an n-symbol address code word; 5. encoding said .[.n-bit.]. .Iadd.n-symbol .Iaddend.address code word using a distance E linear (p,n) code over Galois Field GF(2 m ) to produce p-n redundancy symbols and appending said redundancy symbols to said n-symbol address code word to form a p-symbol address code word such that the p-symbol address code word differs from any other p-symbol address codeword by at least E.[.-1/2 bits.]. .Iadd.symbols and differs from any other p-symbol address code word in a 2 mk neighborhood of said sector by at least D-1 symbols, D-1 .E.Iaddend.; and B. recording said address code words in the sectors during the formatting of the disk; C. reading said address code word from the sector rotating under the head.Iadd., said sector being within a 2 mk neighborhood of the sector to be located; .Iaddend. D. encoding the specified address of the sector to be located in the same manner of step A to produce a specified address code word; E. comparing said sector address code word read from a disk sector with said specified address code word; and F. (1) if the comparison results in a number of symbols which differ between said address code word and said specified address code word that is less than a predetermined number, identifying the sector as the correct sector; or (2) if the comparison results in a number of symbols which differ that is greater than said predetermined number, not identifying the sector as the

Claim 46

separating the sector address containing n m-bit symbols into two segments, a k lower order symbol segment and an n-k higher order symbol segment, 2. using a distance D linear (n,k) code over Galois Field GF(2 m ) to encode said k-symbol segment into an n-symbol code word containing n-k redundancy symbols and the k address symbols .[.such that any two encoded addresses differ by at least D-1/2 symbols.]. .Iadd.such that any two n-symbol code words corresponding to sectors within a 2 mk neighborhood differ in at least D symbols.Iaddend., 3. representing said n-k .[.redundancy.]. .Iadd.higher order .Iaddend.symbol segment in binary Gray code, 4. adding modulo 2 said Gray coded segment to the n-k higher order symbols of said n-symbol code word to produce an n-symbol address code word; 5. encoding said .[.n-bit.]. .Iadd.n-symbol .Iaddend.address code word using a distance E linear (p,n) code over Galois Field GF(2 m ) to produce p-n redundancy symbols and appending said redundancy symbols to said n-symbol address code word to form a p-symbol address code word such that the p-symbol address code word differs from any other p-symbol address codeword by at least E.[.-1/2 bits.]. .Iadd.symbols and differs from any other p-symbol address code word in a 2 mk neighborhood of said sector by at least D-1 symbols, D-1 .E.Iaddend.; and B. recording said address code words in the sectors during the formatting of the disk; C. reading said address code word from the sector rotating under the head.Iadd., said sector being within a 2 mk neighborhood of the sector to be located; .Iaddend. D. encoding the specified address of the sector to be located in the same manner of step A to produce a specified address code word; E. comparing said sector address code word read from a disk sector with said specified address code word; and F. (1) if the comparison results in a number of symbols which differ between said address code word and said specified address code word that is less than a predetermined number, identifying the sector as the correct sector; or (2) if the comparison results in a number of symbols which differ that is greater than said predetermined number, not identifying the sector as the

Claim 47

correct sector. 31. A method for encoding magnetic disk data sector addresses comprising the steps of: A. encoding the addresses of the sectors to produce address code words by: 1. separating the sector address containing n symbols into two segments, a segment containing the k lower order symbols and a segment containing the n-k higher order symbols;

Claim 48

correct sector. 31. A method for encoding magnetic disk data sector addresses comprising the steps of: A. encoding the addresses of the sectors to produce address code words by: 1. separating the sector address containing n symbols into two segments, a segment containing the k lower order symbols and a segment containing the n-k higher order symbols;

Claim 49

using a distance D linear (n,k) code over Galois Field GF(2 m ) to encode said k-symbol segment into an n-symbol code word containing n-k redundancy symbols and the k address symbols .[.such that any two encoded addresses differ by at least D-1/2 symbols.]. .Iadd.such that any two n-symbol code words corresponding to sectors within a 2 mk neighborhood differ in at least D symbols.Iaddend.; 3. representing said n-k .[.redundancy.]..Iadd.higher order .Iaddend.symbol segment in Gray code; 4. adding said Gray coded segment to the n-k higher order symbols of said n-symbol code word to produce an n-symbol address code word; and B. recording said address code words in the sectors during the formatting

Claim 50

using a distance D linear (n,k) code over Galois Field GF(2 m ) to encode said k-symbol segment into an n-symbol code word containing n-k redundancy symbols and the k address symbols .[.such that any two encoded addresses differ by at least D-1/2 symbols.]. .Iadd.such that any two n-symbol code words corresponding to sectors within a 2 mk neighborhood differ in at least D symbols.Iaddend.; 3. representing said n-k .[.redundancy.]..Iadd.higher order .Iaddend.symbol segment in Gray code; 4. adding said Gray coded segment to the n-k higher order symbols of said n-symbol code word to produce an n-symbol address code word; and B. recording said address code words in the sectors during the formatting

Claim 51

of the disk. 32. A method of locating magnetic disk data sectors comprising the steps of: A. reading the address code word recorded in the sector rotating under the head.Iadd., said sector being within a 2 mk neighborhood of the sector to be located; .Iaddend. B. encoding the specified address of the sector to be located by: 1. separating the specified address containing n symbols into two segments, a segment containing k lower order symbols and a segment containing n-k higher order symbols;

Claim 52

of the disk. 32. A method of locating magnetic disk data sectors comprising the steps of: A. reading the address code word recorded in the sector rotating under the head.Iadd., said sector being within a 2 mk neighborhood of the sector to be located; .Iaddend. B. encoding the specified address of the sector to be located by: 1. separating the specified address containing n symbols into two segments, a segment containing k lower order symbols and a segment containing n-k higher order symbols;

Claim 53

using a distance D linear (n,k) code over Galois Field GF(2 m ) to encode said k-symbol segment into an n-symbol code word containing n-k redundancy symbols and the k address symbols; 3. representing said n-k .[.redundancy.]. .Iadd.higher order .Iaddend.symbol segment in Gray code; 4. adding said Gray coded segment to the n-k higher order symbols of said n-symbol code word to produce an n-symbol address code word; C. comparing said specified address code word with the address code word read from a disk sector; and D. (1) if the comparison results in a number of symbols which differ between said address code word and said specified address code word that is less than a predetermined number, identifying the sector as the correct sector; or (2) if the comparison results in a number of symbols which differ that is greater than said predetermined number, not identifying the sector as the

Claim 54

using a distance D linear (n,k) code over Galois Field GF(2 m ) to encode said k-symbol segment into an n-symbol code word containing n-k redundancy symbols and the k address symbols; 3. representing said n-k .[.redundancy.]. .Iadd.higher order .Iaddend.symbol segment in Gray code; 4. adding said Gray coded segment to the n-k higher order symbols of said n-symbol code word to produce an n-symbol address code word; C. comparing said specified address code word with the address code word read from a disk sector; and D. (1) if the comparison results in a number of symbols which differ between said address code word and said specified address code word that is less than a predetermined number, identifying the sector as the correct sector; or (2) if the comparison results in a number of symbols which differ that is greater than said predetermined number, not identifying the sector as the

Claim 55

correct sector. 33. A method for locating data sectors on a magnetic disk during sector seeking operations comprising the steps of: A. encoding the addresses of the sectors to produce address code words by: 1. separating the sector address containing n bits into two segments, a segment containing k lower order bits and a segment containing n-k higher order bits; 2. using a distance D linear code over Galois Field GF(2) to encode said k-bit segment into an n-bit code word containing n-k redundancy symbols and the k address bits .[.such that any two encoded addressed differ by at least D-1/2 bits.]. .Iadd.such that any two n-bit code words corresponding to sectors within a 2 k neighborhood differ in at least D bits; .Iaddend. 3. representing said n-k .[.redundancy symbol.]. .Iadd.higher order bit .Iaddend.segment in Gray code; 4. adding said Gray coded segment to the n-k higher order bits of said n-bit code word to produce an n-bit address code word; 5. encoding said n-bit address code word using a distance E linear (p,n) code over Galois Field GF(2) to produce p-n redundancy symbols and appending said redundancy symbols to said n-bit address code word to form a p-bit address code word such that the p-bit address code word differs from any other p-bit address codeword by at least E.[.-1/2.]. bits .Iadd.and differs from any other p-bit address code word in a 2 k neighborhood of said sector by at least D-1 bits, where D-1.E..Iaddend.; B. recording said address code words in the sectors during the formatting of the disk; C. reading said address code word from the sector rotating under the head.Iadd., said sector being within a 2 k neighborhood of the sector to be located.Iaddend.; D. encoding the specified address of the sector to be located in the same manner of step A to produce a specified address code word; E. comparing said sector address code word read from a disk sector with said specified address code word by adding them using modulo 2 addition; and F. (1) if the comparison results in a number of bits which differ between said address code word and said specified address code word that is less than a predetermined number, identifying the sector as the correct sector; or (2) if the comparison results in a number of bits which differ that is greater than said predetermined number, not identifying the sector as the

Claim 56

correct sector. 33. A method for locating data sectors on a magnetic disk during sector seeking operations comprising the steps of: A. encoding the addresses of the sectors to produce address code words by: 1. separating the sector address containing n bits into two segments, a segment containing k lower order bits and a segment containing n-k higher order bits; 2. using a distance D linear code over Galois Field GF(2) to encode said k-bit segment into an n-bit code word containing n-k redundancy symbols and the k address bits .[.such that any two encoded addressed differ by at least D-1/2 bits.]. .Iadd.such that any two n-bit code words corresponding to sectors within a 2 k neighborhood differ in at least D bits; .Iaddend. 3. representing said n-k .[.redundancy symbol.]. .Iadd.higher order bit .Iaddend.segment in Gray code; 4. adding said Gray coded segment to the n-k higher order bits of said n-bit code word to produce an n-bit address code word; 5. encoding said n-bit address code word using a distance E linear (p,n) code over Galois Field GF(2) to produce p-n redundancy symbols and appending said redundancy symbols to said n-bit address code word to form a p-bit address code word such that the p-bit address code word differs from any other p-bit address codeword by at least E.[.-1/2.]. bits .Iadd.and differs from any other p-bit address code word in a 2 k neighborhood of said sector by at least D-1 bits, where D-1.E..Iaddend.; B. recording said address code words in the sectors during the formatting of the disk; C. reading said address code word from the sector rotating under the head.Iadd., said sector being within a 2 k neighborhood of the sector to be located.Iaddend.; D. encoding the specified address of the sector to be located in the same manner of step A to produce a specified address code word; E. comparing said sector address code word read from a disk sector with said specified address code word by adding them using modulo 2 addition; and F. (1) if the comparison results in a number of bits which differ between said address code word and said specified address code word that is less than a predetermined number, identifying the sector as the correct sector; or (2) if the comparison results in a number of bits which differ that is greater than said predetermined number, not identifying the sector as the

Claim 57

correct sector. 34. An apparatus for locating data sectors on a magnetic disk during sector seeking operations comprising: A. means for encoding the addresses of the sectors to produce address code words, said encoding means including: 1. means for separating the sector address containing n bits into two segments, a segment containing k lower order bits and a segment containing n-k higher order bits; 2. means for using a distance D linear code over Galois Field GF(2) to encode said k-bit segment into an n-bit code word containing n-k redundancy symbols and the k address bits .[.such that any two encoded addressed differ by at least D-1/2 bits.]. .Iadd.such that any two n-bit code words corresponding to sectors within a 2 k neighborhood differ in at least D bits.Iaddend.; 3. means for representing said n-k .[.redundancy symbol.]. .Iadd.higher order bit .Iaddend.segment in Gray code; 4. means for adding said Gray coded segment to the n-k higher order bits of said n-bit code word to produce an n-bit address code word; 5. means for encoding .[.aid.]. .Iadd.said .Iaddend.n-bit address code word using a distance E linear (p,n) code over Galois Field GF(3) to produce p-n redundancy symbols and appending said redundancy symbols to said n-bit address code word to form a p-bit address code word such that the p-bit address code word differs from any other p-bit address codeword by at least E.[.-1/2.]. bits; B. means for recording said address code words in the sectors during the formatting of the disk; C. means for reading said address code word from the sector rotating under the head.Iadd., said sector being within a 2 k neighborhood of the sector to be located; .Iaddend. D. means for encoding the specified address of the sector to be located in the same manner of step A to produce a specified address code word; E. means for comparing said sector address code word read from a disk sector with said specified address code word by adding them using modulo 2 addition; and F. (1) if the comparison results in a number of bits which differ between said address code word and said specified address code word that is less than a predetermined number, means for identifying the sector as the correct sector; and (2) if the comparison results in a number of bits which differ that is greater than said predetermined number, not identifying the sector as the correct sector. .Iadd.35. A method for locating data sectors on a magnetic disk during sector seeking operations comprising the steps of: A. encoding the addresses of the sectors to produce address code words by: 1. separating the sector address containing n bits into two segments, a segment containing the k lower order bits and a segment containing the n-k higher order bits; 2. using a distance D linear (n,k) code over Galois Field GF(2) to encode said k-bit segment into an n-bit code word containing n-k redundancy symbols and the k address bits; 3. representing said n-k higher order bit segment in Gray code; 4. adding said Gray coded segment to the n-k higher order bits of said n-bit code word to produce an n-bit address code word; B. recording said address code words in the sectors during the formatting of the disk; C. reading said address code word from the sector rotating under the head, said sector being within a 2 k neighborhood of the sector to be located; D. encoding the specified address of the sector to be located in the same manner of step A to produce a specified address code word; E. comparing said sector address code word read from a disk sector with said specified address code word; F. (1) if the comparison results in a number of bits which differ between said address code word and said specified address code word that is less than a predetermined number, identifying the sector as the correct sector; or (2) if the comparison results in a number of bits which differ that is greater than said predetermined number, not identifying the sector as the correct sector..Iaddend. .Iadd.36. The method of claim 35 wherein said encoding step further includes encoding said n-bit address code word using a (p,n) distance E linear code over Galois Field GF (2) to produce p-n redundancy symbols and appending said redundancy symbols to said n-bit address code word to form a p-bit address code word..Iaddend. .Iadd.37. A method for locating data sectors on a magnetic disk during sector seeking operations comprising the steps of: A. encoding the addresses of the sectors to produce address code words by: 1. separating the sector address containing n m-bit symbols into two segments, a segment containing the k lower order symbols and a segment containing the n-k higher order symbols; 2. using a distance D linear (n,k) code over Galois Field GF(2 m ) to encode said k-symbol segment into an n-symbol code word containing n-k redundancy symbols and the k address symbols; 3. representing said n-k higher order symbol segment in Gray code; 4. adding said Gray coded segment to the n-k higher order symbols of said n-symbol code word to produce an n-symbol address code word; 5. encoding said n-symbol address code word using a (p,n) distance E linear code over Galois Field GF(2 m ) to produce p-n redundancy symbols and appending said redundancy symbols to said n-symbol address code word to form a p-symbol address code word; B. recording said address code words in the sectors during the formatting of the disk; C. reading said address code word from the sector rotating under the head, said sector being within a 2 mk neighborhood of the sector to be located; D. encoding the specified address of the sector to be located in the same manner of step A to produce a specified address code word; E. comparing said sector address code word read from a disk sector with said specified address code word; F. (1) if the comparison results in a number of symbols which differ between said address code word and said specified address code word that is less than a predetermined number, identifying the sector as the correct sector; or (2) if the comparison results in a number of symbols which differ that is greater than said predetermined number, not identifying the sector as the

Claim 58

correct sector..Iaddend. .Iadd.38. An apparatus for locating data sectors on a magnetic disk during sector seeking operations comprising: A. means for encoding the addresses of the sectors to produce address code words comprising: 1. means for separating the sector address containing n bits into two segments, a k lower order bit segment and an n-k higher order bit segment;

Claim 59

correct sector..Iaddend. .Iadd.38. An apparatus for locating data sectors on a magnetic disk during sector seeking operations comprising: A. means for encoding the addresses of the sectors to produce address code words comprising: 1. means for separating the sector address containing n bits into two segments, a k lower order bit segment and an n-k higher order bit segment;

Claim 60

means for using a distance D linear (n,k) code over Galois Field GF(2) to encode said k-bit segment into an n-bit code word containing n-k redundancy symbols and the k address bits; 3. means for representing said n-k higher order bit segment in Gray code; 4. means for adding said Gray coded segment to the n-k higher order bits of said n-bit code word to produce an n-bit address code word; B. means for recording said address code words in the sectors during the formatting of the disk; C. means for encoding the specified address of the sector to be located in the same manner of step A to produce a specified address code word; D. means for comparing said address code word read from a disk sector which is within a 2 k neighborhood of the sector to be located with said specified address code word; E. (1) if the comparison results in a number of bits which differ between said address code word and said specified address code word that is less than a predetermined number, means for identifying the sector as the correct sector; or (2) if the comparison results in a number of bits which differ that is greater than said predetermined number, not identifying the sector as the

Claim 61

means for using a distance D linear (n,k) code over Galois Field GF(2) to encode said k-bit segment into an n-bit code word containing n-k redundancy symbols and the k address bits; 3. means for representing said n-k higher order bit segment in Gray code; 4. means for adding said Gray coded segment to the n-k higher order bits of said n-bit code word to produce an n-bit address code word; B. means for recording said address code words in the sectors during the formatting of the disk; C. means for encoding the specified address of the sector to be located in the same manner of step A to produce a specified address code word; D. means for comparing said address code word read from a disk sector which is within a 2 k neighborhood of the sector to be located with said specified address code word; E. (1) if the comparison results in a number of bits which differ between said address code word and said specified address code word that is less than a predetermined number, means for identifying the sector as the correct sector; or (2) if the comparison results in a number of bits which differ that is greater than said predetermined number, not identifying the sector as the

Claim 62

correct sector..Iaddend. .Iadd.39. The apparatus of claim 38 wherein said encoding means further comprises means for encoding said n-bit address code word using a (p,n) distance E linear code over Galois Field GF(2) to produce p-n redundancy symbols and appending said redundancy symbols to said n-bit address code word to form a p-bit address code word..Iaddend. .Iadd.40. An apparatus for locating a sector on a magnetic disk comprising: A. means for reading an address code word from the sector rotating under the head; B. means for encoding the specified address of the sector to be located to produce an address code word comprising: 1. means for separating the sector address containing n bits into two segments, a k lower order bit segment and an n-k higher order bit segment; 2. means for using a distance D linear (n,k) code over Galois Field GF(2) to encode said k-bit segment into an n-bit code word containing n-k redundancy symbols and the k address bits; 3. means for representing said n-k higher order bit segment in Gray code; 4. means for adding said Gray coded segment to the n-k higher order bits of said n-bit code word to produce an n-bit address code word; C. means for comparing said specified address code word with the sector address code word read from a disk sector, said disk sector being within a 2 k neighborhood of the sector be to located; D. (1) if the comparison results in a number of bits which differ between said address code word and said specified address code word that is less than a predetermined number, identifying the sector as the correct sector; or (2) if the comparison results in a number of bits which differ that is greater than said predetermined number, not identifying the sector as the

Claim 63

correct sector..Iaddend. .Iadd.41. The apparatus of claim 40 wherein said encoding means further comprises means for encoding said n-bit address code word using a distance E linear (p,n) code over Galois Field GF(2) to produce p-n redundancy symbols and appending said redundancy symbols to said n-bit address code word to form a p-bit address code word..Iaddend. .Iadd.42. A method for encoding magnetic disk data sector addresses comprising the steps of: A. encoding the addresses of the sectors to produce address code words by: 1. separating the sector address containing n symbols into two segments, a segment containing the k lower order symbols and a segment containing the n-k higher order symbols; 2. using a distance D linear (n,k) code over Galois Field GF(2 m ) to encode said k-symbol segment into an n-symbol code word containing n-k redundancy symbols and the k address symbols; 3. representing said n-k higher order symbol segment in Gray code; 4. adding said Gray coded segment to the n-k higher order symbols of said n-symbol code word to produce an n-symbol address code word; and B. recording said address code words in the sectors during the formatting of the disk..Iaddend. .Iadd.43. An apparatus for encoding magnetic disk sector addresses comprising: A. means for encoding the addresses of the sectors to produce address code words by: 1. separating the sector address containing n bits into two segments, a segment containing k lower order bits and a segment containing n-k higher order bits; 2. means for using a distance D linear code over Galois Field GF(2) to encode said k-bit segment into an n-bit code word containing n-k redundancy symbols and the k address bits;

Claim 64

means for representing said n-k higher order bit segment in Gray code; 4. means for adding said Gray coded segment to the n-k higher order bits of said n-bit code word to produce an n-bit address code word; and B. means for recording said address code words in the sectors during the formatting of the disk..Iaddend. .Iadd.44. The method of claim 5, wherein said encoding step further includes encoding said n-symbol address code word using a (p,n) distance E linear code over Galois Field GF(2 m ) to produce p-n redundancy symbols and appending said redundancy symbols to said n-symbol address code word to form a p-symbol address code word such that the p-symbol address code word differs from any other p-symbol address codeword by at least E symbols..Iaddend. .Iadd.45. The method of claim 31 wherein said encoding step further includes encoding said n-symbol address code word using a (p,n) distance E linear code over Galois Field GF(2 m ) to produce p-n redundancy symbols and appending said redundancy symbols to said n-symbol address code word to form a p-symbol address code word such that the p-symbol address code word differs from any other p-symbol address codeword by at least E symbols..Iaddend.