Generalization of the Lee-O'Sullivan List Decoding for One-Point AG Codes

Abstract

We generalize the list decoding algorithm for Hermitian codes proposed by Lee and O'Sullivan based on Gr\"obner bases to general one-point AG codes, under an assumption weaker than one used by Beelen and Brander. Our generalization enables us to apply the fast algorithm to compute a Gr\"obner basis of a module proposed by Lee and O'Sullivan, which was not possible in another generalization by Lax.Comment: article.cls, 14 pages, no figure. The order of authors was changed. To appear in Journal of Symbolic Computation. This is an extended journal paper version of our earlier conference paper arXiv:1201.624