Groebner bases and combinatorics for binary codes

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dc.creatorBorges-Quintana, M.
dc.creatorBorges-Trenard, M. A.
dc.creatorFitzpatrick, P.
dc.creatorMartinez-Moro, E.
dc.date2005-09-08
dc.date.accessioned2026-07-07T05:23:01Z
dc.date.available2026-07-07T05:23:01Z
dc.descriptionIn 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. 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.
dc.descriptionSubmitted to Appl. Algebra Engrg. Comm. Comput
dc.identifierhttps://arxiv.org/abs/math/0509164
dc.identifierhttp://arxiv.org/abs/math/0509164
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76284
dc.subjectCombinatorics
dc.subjectCommutative Algebra
dc.subject13P10 ; 94B05
dc.titleGroebner bases and combinatorics for binary codes
dc.typetext

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