Browsing by Subject "Reed Muller codes"

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    New advances in permutation decoding of first-order Reed-Muller codes
    (Elsevier, 2023) Bernal Buitrago, José Joaquín; Matemáticas
    In this paper we describe a variation of the classical permutation decoding algorithm that can be applied to any affine-invariant code with respect to certain type of information sets. In particular, we can apply it to the family of first-order Reed-Muller codes with respect to the information sets introduced in \cite{BS}. Using this algortihm we improve considerably the number of errors we can correct in comparison with the known results in this topic.
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    Permutation decoding of first-order Generalized Reed-Muller codes
    (2025) Bernal Buitrago, José Joaquín; Simón Pinero, Juan Jacobo; Matemáticas
    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-order Reed-Muller codes successfully. In this paper we study how to implement it for the family of first-order Generalized Reed-Muller codes.Then, we give examples which show that we improve the number of errors we can correct in comparison with the known results for this family of codes. Finally, we deal, from a probabilistic point of view, with the problem of determining when the algorithm only needs to use a smaller PD-like set.