Method and apparatus for encoding and mapping magnetic disk sector addresses

Claim 1

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 "k"-bit lower order bit segment and an (n-k)-bit higher order bit segment; 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)-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; 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.

Claim 2

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 "k"-bit lower order bit segment and an (n-k)-bit higher order bit segment; 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)-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; 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.

Claim 5

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" multi-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; 3. representing said (n-k) high order symbol segment in binary Gray code; 4. exclusive OR'ing said Gray coded segment to the n-­k high 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; 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 6

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" multi-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; 3. representing said (n-k) high order symbol segment in binary Gray code; 4. exclusive OR'ing said Gray coded segment to the n-­k high 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; 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 8

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" low order bit segment and an (n-k) high 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)-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 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 9

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" low order bit segment and an (n-k) high 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)-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 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 12

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" multi-bit symbols into two segments, a "k" lower order symbol segment and an (n-k) higher order symbol segment, 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, 3. means for representing said (n-k)-symbol segment in binary Gray code, 4. means for exclusive OR'ing 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. 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; 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; 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 13

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" multi-bit symbols into two segments, a "k" lower order symbol segment and an (n-k) higher order symbol segment, 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, 3. means for representing said (n-k)-symbol segment in binary Gray code, 4. means for exclusive OR'ing 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. 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; 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; 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 16

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" bits into two segments, a "k"-bit lower order bit segment and an (n-k)-bit higher order bit segment; 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)-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; and B. recording said address code words in the sectors during the formatting of the disk.

Claim 17

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" bits into two segments, a "k"-bit lower order bit segment and an (n-k)-bit higher order bit segment; 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)-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; and B. recording said address code words in the sectors during the formatting of the disk.

Claim 19

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" low order bit segment and an (n-k) high 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)-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.

Claim 20

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" low order bit segment and an (n-k) high 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)-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.

Claim 22

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 specified address containing "n" bits into two segments, a "k" low order bit segment and an (n-k) high 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)-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; 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 correct sector.

Claim 23

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 specified address containing "n" bits into two segments, a "k" low order bit segment and an (n-k) high 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)-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; 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 correct sector.

Claim 26

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 "k"-bit lower order bit segment and an (n-k)-bit higher order bit segment; 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)-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; 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 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.

Claim 27

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 "k"-bit lower order bit segment and an (n-k)-bit higher order bit segment; 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)-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; 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 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.

Claim 30

An apparatus for encoding magnetic disk 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" multi-bit symbols into two segments, a "k" lower order symbol segment and an (n-k) higher order symbol segment; 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; 3. means for representing said (n-k)-bit segment in binary Gray code; 4. means for exlcusive OR'ing said Gray coded segment to the n-k higher order bits of said n-symbol code word to produce and n-symbol address code word; and B. means for recording said address code words in the sectors during the formatting of the disk;

Claim 31

An apparatus for encoding magnetic disk 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" multi-bit symbols into two segments, a "k" lower order symbol segment and an (n-k) higher order symbol segment; 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; 3. means for representing said (n-k)-bit segment in binary Gray code; 4. means for exlcusive OR'ing said Gray coded segment to the n-k higher order bits of said n-symbol code word to produce and n-symbol address code word; and B. means for recording said address code words in the sectors during the formatting of the disk;

Claim 33

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" multi-bit symbols into two segments, a "k" lower order symbol segment and an (n-k) higher order symbol segment, 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, 3. means for representing said (n-k)-symbol segment in binary Gray code, 4. means for exclusive OR'ing 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. comparison means for comparing said sector address code word read from a disk sector with said specified code word; 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, 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 correct sector.

Claim 34

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" multi-bit symbols into two segments, a "k" lower order symbol segment and an (n-k) higher order symbol segment, 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, 3. means for representing said (n-k)-symbol segment in binary Gray code, 4. means for exclusive OR'ing 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. comparison means for comparing said sector address code word read from a disk sector with said specified code word; 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, 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 correct sector.

Claim 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" multi-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 in the k address symbols, 3. representing said (n-k)-symbol segment in binary Gray code, 4. exclusive OR'ing 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 address code word using a (p,n) distance "E" linear code over Galois Field GF(2 m ) to produce redundancy symbols and appending said redundancy symbols to said address code word to form another 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; D. encoding the specified address of the sector to be located in the same manner of step A to produce a specified 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 correct sector;

Claim 38

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" multi-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 in the k address symbols, 3. representing said (n-k)-symbol segment in binary Gray code, 4. exclusive OR'ing 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 address code word using a (p,n) distance "E" linear code over Galois Field GF(2 m ) to produce redundancy symbols and appending said redundancy symbols to said address code word to form another 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; D. encoding the specified address of the sector to be located in the same manner of step A to produce a specified 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 correct sector;

Claim 39

A method for encoding magnetic disk 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" multi-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, 3. representing said (n-k)-symbol segment in binary Gray code; 4. exclusive OR'ing said Gray coded segment to the n-k higher order bits 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.

Claim 40

A method for encoding magnetic disk 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" multi-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, 3. representing said (n-k)-symbol segment in binary Gray code; 4. exclusive OR'ing said Gray coded segment to the n-k higher order bits 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.

Claim 42

A method for locating sectors on a magnetic disk comprising the steps of: A. reading an address code word from the sector rotating under the head; B. encoding the specified address of the sector to be located by: 1. separating the sector address containing "n" multi-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, 3. representing said (n-k)-symbol segment in binary Gray code; 4. exclusive OR'ing said Gray coded segment to the n-k higher order symbols of said n-symbol code word to produce an n-bit address code word; C. comparing said sector address code word read from a disk sector with said specified address code word; 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 correct sector.

Claim 43

A method for locating sectors on a magnetic disk comprising the steps of: A. reading an address code word from the sector rotating under the head; B. encoding the specified address of the sector to be located by: 1. separating the sector address containing "n" multi-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, 3. representing said (n-k)-symbol segment in binary Gray code; 4. exclusive OR'ing said Gray coded segment to the n-k higher order symbols of said n-symbol code word to produce an n-bit address code word; C. comparing said sector address code word read from a disk sector with said specified address code word; 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 correct sector.

Claim 46

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 "k"-bit lower order bit segment and an (n-k)-bit higher order bit segment; 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) 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; 5. encoding said n-bit address code word using a (p,n) distance "E" linear code over Galois Field GF(2) to produce redundancy symbols and appending said redundancy symbols to said 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; 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.

Claim 47

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 "k"-bit lower order bit segment and an (n-k)-bit higher order bit segment; 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) 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; 5. encoding said n-bit address code word using a (p,n) distance "E" linear code over Galois Field GF(2) to produce redundancy symbols and appending said redundancy symbols to said 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; 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.

Claim 48

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" multi-bit symbols into two segments, a "k" lower order symbol segment and an (n-k) higher order symbol segment, 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, 3. means for representing said (n-k)-symbol segment in binary Gray code, 4. means for exclusive OR'ing 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. means for encoding said n-bit address code word using a (p,n) distance "E" linear code over Galois Field GF(2 m ) to produce redundancy symbols and appending said redundancy symbols to said address code word to form another address code word; 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; D. means for encoding the specified address of the sector to be located using said encoding means; E. comparing means for 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 that said predetermined number, not identifying the sector as the correct sector.

Claim 49

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" multi-bit symbols into two segments, a "k" lower order symbol segment and an (n-k) higher order symbol segment, 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, 3. means for representing said (n-k)-symbol segment in binary Gray code, 4. means for exclusive OR'ing 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. means for encoding said n-bit address code word using a (p,n) distance "E" linear code over Galois Field GF(2 m ) to produce redundancy symbols and appending said redundancy symbols to said address code word to form another address code word; 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; D. means for encoding the specified address of the sector to be located using said encoding means; E. comparing means for 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 that said predetermined number, not identifying the sector as the correct sector.

Claim 50

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 symbol segment and an (n-k) higher order segment, 2. means for using a distance "D" linear (n,k) code over Galois Field GF( m ) 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)-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; 5. means for encoding said n-bit address code word using a (p,n) distance "E" linear code over Galois Field GF(2) to produce redundancy symbols and appending said redundancy symbols to said 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 froma disk sector 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 that said predetermined number, not identifying the sector as the correct sector.

Claim 51

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 symbol segment and an (n-k) higher order segment, 2. means for using a distance "D" linear (n,k) code over Galois Field GF( m ) 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)-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; 5. means for encoding said n-bit address code word using a (p,n) distance "E" linear code over Galois Field GF(2) to produce redundancy symbols and appending said redundancy symbols to said 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 froma disk sector 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 that said predetermined number, not identifying the sector as the correct sector.