Edgar Martínez-Moro

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In 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(More)
This article aims to explore the bridge between the algebraic structure of a linear code and the complete decoding process. To this end, we associate a specific binomial ideal I+(C) to an arbitrary linear code. The binomials involved in the reduced Gröbner basis of such an ideal relative to a degreecompatible ordering induce a uniquely defined test-set for(More)
Niederreiter and Xing (2000) recently proposed a propagation rule for linear codes.O/spl uml/zbudak and Stichtenoth showed that the Niederreiter-Xing construction is a particular construction of a matrix-product code. Cheng, Cheng, and Sun analyzed the case when Niederreiter-Xing rule commutes with duality. The aim of this correspondence is to generalize(More)
This paper addresses the question of how often the square code of an arbitrary l-dimensional subcode of the code GRSk(a,b) is exactly the code GRS2k−1(a,b ∗ b). To answer this question we first introduce the notion of gaps of a code which allows us to characterize such subcodes easily. This property was first stated and used in [10] where Wieschebrink(More)
It has been widely known that complete decoding for binary linear codes can be regarded as an linear integer programming problem with binary arithmetic conditions. Conti and Traverso [8] have proposed an efficient algorithm which uses Gröbner bases to solve integer programming with ordinary integer arithmetic conditions. Ikegami and Kaji [11] extended the(More)
This paper addresses the question of retrieving the triple (X ,P, E) from the algebraic geometry code C = CL(X ,P, E), where X is an algebraic curve over the finite field Fq, P is an n-tuple of Fq-rational points on X and E is a divisor on X . If deg(E) ≥ 2g + 1 where g is the genus of X , then there is an embedding of X onto Y in the projective space of(More)
In this work we consider repeated-root multivariable codes over a finite chain ring. We show conditions for these codes to be principally generated. We consider a suitable set of generators of the code and compute its minimum distance. As an application we study the relevant example of the generalized Kerdock code in its r -dimensional cyclic version.