Generalization of the Lee-O'Sullivan List Decoding for One-Point AG Codes
Information Theory
2013-04-22 v5 Symbolic Computation
Commutative Algebra
Algebraic Geometry
math.IT
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.
Cite
@article{arxiv.1203.6129,
title = {Generalization of the Lee-O'Sullivan List Decoding for One-Point AG Codes},
author = {Ryutaroh Matsumoto and Diego Ruano and Olav Geil},
journal= {arXiv preprint arXiv:1203.6129},
year = {2013}
}
Comments
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:1201.6248