Error correction method using Reed-Solomon code

Claim 2

An error-correction method for use in decoding Reed-Solomon code that corrects errors in data by use of known error locations, whereby respective error symbols are corrected by use of n error vectors obtained by a series of steps comprising: (A) performing product sum arithmetic operations of syndromes Sν(ν=0 to n-1) and error locations X j (j=1 to n) on the basis of: Sν.sub.,i =Sν.sub.,i-1 X.sub.i +Sν.sub.+1,i-1 ( 1≦i≦n-1: n is the number of error symbols) where, (Sν.sub.,0 =Sν) for sequentially obtaining an i th answer Sν.sub.,i, and for finally obtaining S 0 ,n-1 ; and (B) obtaining error vectors Y n by performing the following arithmetic operation by use of said S O ,n-1, ##EQU23##

Claim 3

An error correction method for use in decoding Reed-Solomon code that corrects errors by use of known error locations, whereby respective error symbols are corrected by use of n error vectors obtained by repetitively executing a series of steps comprising: (A) performing product sum arithmetic operations of syndromes Sν(ν=0 to n-1) and error locations X j (j=1 to n) on the basis: Sν.sub.,i =Sν.sub.,i-1 X.sub.i +Sν.sub.+1,i-l ( 1≦i≦n-1: and n is the number of error symbols) where, (Sν.sub.,0 =S); for sequentially obtaining an i th answer Sν.sub.,i, and for finally obtaining S 0 ,n-1 ; (B) obtaining error vectors Y n by performing the following arithmetic operation by use of said S 0 ,n-1 derived in the preceding step, ##EQU24## thereby correcting one-symbol errors; (C) correcting said syndromes Sν(ν=0 to n-2) by use of said error vectors Y n , thereby producing syndromes in the case of (n-1)-multiple errors; and (D) thereafter, applying said equation for Sν.sub.,i to obtain the next error vector Y n-1 .

Claim 4

An error correction method for use in decoding Reed-Solomon code that corrects errors by use of known error locations, whereby respective error symbols are corrected by use of n error vectors obtained by repetitively executing a series of steps comprising: (A) performing product sum arithmetic operations of syndromes Sν(ν=0 to n-1) and error locations X j (j=1 to n) on the basis: Sν.sub.,i =Sν.sub.,i-1 X.sub.i +Sν.sub.+1,i-l ( 1≦i≦n-1: and n is the number of error symbols) where, (Sν.sub.,0 =S); for sequentially obtaining an i th answer Sν.sub.,i, and for finally obtaining S 0 ,n-1 ; (B) obtaining error vectors Y n by performing the following arithmetic operation by use of said S 0 ,n-1 derived in the preceding step, ##EQU24## thereby correcting one-symbol errors; (C) correcting said syndromes Sν(ν=0 to n-2) by use of said error vectors Y n , thereby producing syndromes in the case of (n-1)-multiple errors; and (D) thereafter, applying said equation for Sν.sub.,i to obtain the next error vector Y n-1 .