Groebner bases and combinatorics for binary codes
组合数学
2007-05-23 v1 交换代数
摘要
In this paper we introduce a binomial ideal derived from a binary linear code. We present some applications of a Gr\"obner basis of this ideal with respect to a total degree ordering. In the first application we give a decoding method for the code. By associating the code with the set of cycles in a graph, we can solve the problem of finding all codewords of minimal length (minimal cycles in a graph), and show how to find a minimal cycle basis. Finally we discuss some results on the computation of the Gr\"obner basis.
引用
@article{arxiv.math/0509164,
title = {Groebner bases and combinatorics for binary codes},
author = {M. Borges-Quintana and M. A. Borges-Trenard and P. Fitzpatrick and E. Martinez-Moro},
journal= {arXiv preprint arXiv:math/0509164},
year = {2007}
}
备注
Submitted to Appl. Algebra Engrg. Comm. Comput