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 …

In this paper we use the Gröbner representation of a binary linear code to give efficient
algorithms for computing the whole set of coset leaders, denoted by and the set of leader …

We specialize Möller's algorithm to the computation of Gröbner bases related to lattices. We
give the complexity analysis of our algorithm. Then we provide experiments showing that our …

There are two gradient descent decoding procedures for binary codes proposed
independently by Liebler and by Ashikhmin and Barg. Liebler in his paper mentions that …

Esta tesis pretende explorar el nexo de unión que existe entre la estructura algebraica de
un código lineal y el proceso de descodificación completa. Sabemos que el proceso de …

Several constructions in binary linear block codes are also related to matroid theory topics.
These constructions rely on a given order in the ground set of the matroid. In this paper we …

In this work, we show the connections between trial sets and Gröbner bases for binary
codes, which give characterizations of trial sets in the context of Gröbner bases and …

We present an algorithm for computing the set of all coset leaders of a binary code $\mathcal
C\subset\mathbb {F} _2^ n $. The method is adapted from some of the techniques related to …

Los avances científicos y tecnológicos han supuesto cambios muy rápidos. Se suceden de
forma acelerada, no dando lugar a que el hombre pueda interiorizarlos y adaptarse a las …