The correction capability of the Berlekamp-Massey-Sakata algorithm with majority voting

Sakata's generalization of the Berlekamp-Massey algorithm applies to a broad class of codes defined by an evaluation map on an order domain. In order to decode up to the minimum distance bound, Sakata's algorithm must be combined with the majority voting algorithm of Feng, Rao and Duursma. This combined algorithm can often decode far more than (d min -1)/2 errors, provided the errors are in general position. We give a precise characterization of the error correction capability of the combined algorithm. We also extend the concept behind Feng and Rao's improved codes to decoding of errors in general position. The analysis leads to a new characterization of Arf numerical semigroups. © Springer-Verlag 2006.