5 papers · 1 filter
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…
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…
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…