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 …

In this paper, a new low-complexity gradient-descent based iterative majority-logic decoder
(GD-MLGD) is proposed for decoding One-Step Majority-Logic Decodable (OSMLD) codes …

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 …

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 …

In order to obtain the set of codewords of minimal support for codes defined over Z _q, one
can compute a Graver basis of the ideal associated to such codes. The main aim of this …

There is a deep connection between linear codes and combinatorial designs. Combinatorial
designs can give rise to linear codes and vice versa. In particular, perfect codes always hold …

Each linear code can be described by a so-called code ideal. In order to utilize this ideal,
Gröbner bases are required. Since many results depend on the chosen term order …

In this paper, soft-input/soft-output decoding of an arbitrary linear block error correction code
over any finite field is performed by transforming an algebraic description of the decoding …

In order to obtain the set of codewords of minimal support of codes defined over Zq we must
compute a Graver basis of the ideal associated to such codes, see [9]. The main aim of this …