List Decoding Algorithms based on Groebner Bases for General 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. By using the same principle, we also generalize the unique decoding algorithm for one-point AG codes over the Miura-Kamiya curves proposed by Lee, Bras-Amor\'os and O'Sullivan 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 that has not been done in the original proposal, and remove the unnecessary computational steps so that it can run faster.
Keywords
Cite
@article{arxiv.1201.6248,
title = {List Decoding Algorithms based on Groebner Bases for General One-Point AG Codes},
author = {Olav Geil and Ryutaroh Matsumoto and Diego Ruano},
journal= {arXiv preprint arXiv:1201.6248},
year = {2012}
}
Comments
IEEEtran.cls, 5 pages, no figure. To appear in Proc. 2012 IEEE International Symposium on Information Theory, July 1-6, 2012, Boston, MA, USA. Version 4 corrected wrong description of the work by Lee, Bras-Amor\'os and O'Sullivan, and added four references