A GENERALIZED FORNEY FORMULA FOR ALGEBRAIC-GEOMETRIC CODES

This correspondence contains a straightforward generalization of decod ing of BCH codes to the decoding of algebraic-geometric codes, couched in terms of varieties, ideals, and Grobner bases. This consists of 1) a Berlekamp-Massey-type lattice-shifting row-reduction algorithm with majority voting similar to algorithms in the current literature, 2) a realization that it produces a minimal Grobner basis B for the error- locator ideal I(V) relative to a particular weighted total degree mono mial ordering, 3) a factoring of that basis into several minimal PLEX bases, that facilitates finding the variety V of error positions, and 4) a direct generalization of Forney's formula to calculate error magn itudes using functions sigma p, which are by-products of this factorin g.