List decoding algorithms based on Gröbner bases for general one-point AG codes

摘要

We generalize the list decoding algorithm for Hermitian codes proposed by Lee and O''Sullivan [15] based on Gröbner bases to general one-point AG codes, under an assumption weaker than one used by Beelen and Brander [4]. By using the same principle, we also generalize the unique decoding algorithm for one-point AG codes over the Miura-Kamiya Cab curves proposed by Lee, Bras-Amorós and O''Sullivan [14] to general one-point AG codes, without any assumption. Finally we extend the latter unique decoding algorithm to list decoding, modify it so that it can be used with the Feng-Rao improved code construction, prove equality between its error correcting capability and half the minimum distance lower bound by Andersen and Geil [3] that has not been done in the original proposal, and remove the unnecessary computational steps so that it can run faster.