2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76284In 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.Submitted to Appl. Algebra Engrg. Comm. ComputCombinatoricsCommutative Algebra13P10 ; 94B05text