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TitleGr\"obner bases and combinatorics for binary codes.
Author(s) Mijail Borges-Quintana, Miguel A. Borges-Trenard, Patrick Fitzpatrick, Edgar Martinez-Moro
TypeArticle in Journal
AbstractIn this paper we introduce a binomial ideal derived from a binary linear code. We present some applications of a Gröbner basis of this ideal with respect to a total degree ordering. In the first application we give a decoding method for the code. In the second one, 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 Gröbner basis.
KeywordsBinary codes, Cycle bases, Gröbner bases
ISSN0938-1279; 1432-0622/e
URL http://link.springer.com/article/10.1007%2Fs00200-008-0080-2
JournalAppl. Algebra Eng. Commun. Comput.
PublisherSpringer, Berlin/Heidelberg
Translation No
Refereed No