Browsing by Subject "Abelian codes"
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- PublicationOpen AccessA new approach to the Berlekamp-Massey-Sakata Algorithm. Improving Locator Decoding(IEEE, 2021) Bernal Buitrago, José Joaquín; Simón Pinero, Juan Jacobo; MatemáticasWe study the problem of the computation of Groebner basis for the ideal of linear recurring relations of a doubly periodic array. We find a set of indexes such that, along with some conditions, guarantees that the set of polynomials obtained at the last iteration in the Berlekamp-Massey-Sakata algorithm is exactly a Groebner basis for the mentioned ideal. Then, we apply these results to improve locator decoding in abelian codes.
- PublicationOpen AccessA note on the theoretical support to compute dimension in Abelian codes(2024) Bernal Buitrago, José Joaquín; Simón Pinero, Juan Jacobo; MatemáticasIn this note we give a theoretical support by means of quotient polynomial rings for the computation formulas of the dimension of abelian codes.
- PublicationOpen AccessInference of unknown syndrome values in the implementation of the Berlekamp-Massey-Sakata algorithm.(2025) Bernal Buitrago, José Joaquín; Simón Pinero, Juan Jacobo; Matemáticas
- PublicationOpen AccessInformation sets from defining sets for Reed-Muller codes of first and second order(IEEE, 2018) Bernal Buitrago, José Joaquín; Simón Pinero, Juan Jacobo; MatemáticasReed-Muller codes belong to the family of affine-invariant codes. As such codes they have a defining set that determines them uniquely, and they are extensions of cyclic group codes. In this paper we identify those cyclic codes with multidimensional abelian codes and we use the techniques introduced in \cite{BS} to construct information sets for them from their defining set. For first and second order Reed-Muller codes, we describe a direct method to construct information sets in terms of their basic parameters.
- PublicationEmbargoInformation sets from defining sets in abelian codes(Institute of Electrical and Electronics Engineers, 2011-09) Bernal Buitrago, José Joaquín; Simón Pinero, Juan Jacobo; MatemáticasWe 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 by Imai in the case of binary TDC codes.