Browsing by Subject "Information sets"
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- 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.