Patent ID: 7392454
Filing Date: 2008-06-24
Classification: H03M

Abstract:
1. A method of decoding a one-point algebraic geometric code of dimension k and length n, said algebraic geometric code being constructed on a locating set of which elements are pairs (x, y) that are solutions of an algebraic equation with two unknowns X and Y defining a curve of non-zero genus, in which, in order to identify a position of errors in a received word, a syndromes matrix S, of dimension (n−k)×(n−k) is defined, of which elements S ij of each line i are calculated, for j between 1 and w(i), wherein the boundary w is a decreasing function, using a syndrome s of the received word, said method comprising the following steps: producing the syndromes matrix S from the received word; implementing a first stage of a two-stage decoding algorithm applied to the matrix S, to obtain a set of first stage locating-candidate polynomials including polynomials in X and Y; searching in the set of first stage locating-candidate polynomials for whether there is a polynomial in X only; and decoding the received word, if there is a polynomial in X only, using the polynomial in X only as a locating polynomial in X.