Error-locator ideals for algebraic-geometric codes
D.A. Leonard · IEEE Transactions on Information Theory · 1995
The error locations for an algebraic-geometric code C*(D,mP) are exactly the common zeros (that is, a projective variety V(I)) of a set (ideal) I of error-locator functions. The paper gives a one-dimensional Berlekamp-Massey version of the Feng-Rao (1993) algorithm for decoding algebraic-geometric codes C*(D,mP). This produces a generating set for I (as an ideal) of size at most /spl rho/ (the smallest positive pole order at P of any function in L(mP)) relative to any error of weight at most e>