Patent ID: 6199088
Filing Date: 2001-03-06
Classification: G06F

Abstract:
A method for correcting errors in a code word encoded over a Galois Field GF(2.sup.2M) and 2M+1 is prime, the method including the steps of:A. decoding the codeword and performing Galois Field division operations involving Galois Field elements B and A byi. representing A as a (2M+1)-bit symbol;ii. producing an (M+1)-bit representation of an element C=A.sup.2.sup..sup.M+1 by calculatingc.sub.0 =.SIGMA.a.sub.i a.sub.ic.sub.1 =.SIGMA.a.sub.i a.sub.i+1c.sub.2 =.SIGMA.a.sub.i a.sub.i+2c.sub.M.SIGMA.=a.sub.i a.sub.i+Mwhere the a.sub.j 's are coefficients of a (2M+1)-bit representation of A and the c.sub.j 's are coefficients of C;iii. using the M+1 bits representing C to determine C.sup.-1 ;iv. multiplying C.sup.-1 by A.sup.2.sup..sup.M ;v. multiplying A.sup.-1 by B; andB. determining the locations of errors in the code word using the quotients B/A.