4 citations · 4 across the 6 of their papers we have counts for
6 papers
On the weak order ideal associated to linear codes
M. Borges-Quintana, M. A. Borges-Trenard, E. Martinez-Moro
In this work we study a weak order ideal associated with the coset leaders of a non-binary linear code. This set allows the incrementally computation of the coset leaders and the d…
On zero neighbours and trial sets of linear codes
Mijail Borges-Quintana, Miguel Angel Borges-Trenard, Edgar Martinez-Moro
In this work we study the set of leader codewords of a non-binary linear code. This set has some nice properties related to the monotonicity of the weight compatible order on the g…
Computing coset leaders of binary codes
M. Borges-Quintana, M. A. Borges-Trenard, E. Martinez-Moro
We present an algorithm for computing the set of all coset leaders of a binary code . The method is adapted from some of the techniques related t…
A general framework for applying FGLM techniques to linear codes
M. Borges-Quintana, M. A. Borges-Trenard, E. Martinez-Moro
We show herein that a pattern based on FGLM techniques can be used for computing Gröbner bases, or related structures, associated to linear codes. This Gröbner bases setting turns…
Groebner bases and combinatorics for binary codes
M. Borges-Quintana, M. A. Borges-Trenard, P. Fitzpatrick +1
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…
On a Grobner bases structure associated to linear codes
M. Borges-Quintana, M. Borges-Trenard, E. Martinez-Moro
We present a structure associated to the class of linear codes. The properties of that structure are similar to some structures in the linear algebra techniques into the framework…