1 citations · 1 across the 13 of their papers we have counts for
13 papers
A Note on the Theoretical Support to Compute Dimension in Abelian Codes
J. J. Bernal, J. J. Simón
In this note we give a theoretical support by means of quotient polynomial rings for the computation formulas of the dimension of abelian codes.
Hyperbolic Sets in Incomplete Tables
J. J. Bernal, J. J. Simón
In this paper, we extend results about the implementation of the Berlekamp-Massey-Sakata algorithm on data tables having a number of unknown values.
Permutation decoding of first-order Generalized Reed-Muller codes
José Joaquín Bernal, Juan Jacobo Simón
In [4] we describe a variation of the classical permutation decoding algorithm that can be applied to any binary affine-invariant code; in particular, it can be applied to first-or…
Constructions of Abelian Codes multiplying dimension of cyclic codes
José Joaquín Bernal, Diana H. Bueno-Carreño, Juan Jacobo Simón
In this note, we apply some techniques developed in [1]-[3] to give a particular construction of bivariate Abelian Codes from cyclic codes, multiplying their dimension and preservi…
Cyclic and BCH Codes whose Minimum Distance Equals their Maximum BCH bound
José Joaquín Bernal, Diana H. Bueno-Carreño, Juan Jacobo Simón
In this paper we study the family of cyclic codes such that its minimum distance reaches the maximum of its BCH bounds. We also show a way to construct cyclic codes with that prope…
Apparent Distance and a Notion of BCH Multivariate Codes
José Joaquín Bernal, Diana H. Bueno-Carreño, Juan Jacobo Simón
This paper is devoted to studying two main problems: 1) computing the apparent distance of an Abelian code and 2) giving a notion of Bose, Ray-Chaudhuri, Hocquenghem (BCH) multivar…
An intrinsical description of group codes
José Joaquín Bernal, Ángel del Río, Juan Jacobo Simón
A (left) group code of length n is a linear code which is the image of a (left) ideal of a group algebra via an isomorphism from FG to Fn which maps G to the standard basis of Fn.…
From ds-bounds for cyclic codes to true distance for abelian codes
J. J. Bernal, M. Guerreiro, J. J. Simón
In this paper we develop a technique to extend any bound for the minimum distance of cyclic codes constructed from its defining sets (ds-bounds) to abelian (or multivariate) codes…
Ds-bounds for cyclic codes: new bounds for abelian codes
J. J. Bernal, M. Guerreiro, J. J. Simón
In this paper we develop a technique to extend any bound for cyclic codes constructed from its defining sets (ds-bounds) to abelian (or multivariate) codes. We use this technique t…
Information sets from defining sets in abelian codes
José Joaquín Bernal, Juan Jacobo Simón
We describe a technique to construct a set of check positions (and hence an information set) for every abelian code solely in terms of its defining set. This generalizes that given…
Globalization of twisted partial actions
M. Dokuchaev, R. Exel, J. J. Simón
Let A be a unital ring which is a product of possibly infinitely many indecomposable rings. We establish criteria for the existence of a globalization for a given twisted partial a…
Group code structures on affine-invariant codes
Jose Joaquin Bernal, Angel del Rio, Juan Jacobo Simon
A group code structure of a linear code is a description of the code as one-sided or two-sided ideal of a group algebra of a finite group. In these realizations, the group algebra…
Crossed products by twisted partial actions and graded algebras
M. Dokuchaev, R. Exel, J. J. Simon
For a twisted partial action Θof a group G on an (associative non-necessarily unital) algebra A over a commutative unital ring k, the crossed product A X_ΘG is proved to be associa…