2025/09/15 by José Joaquín Bernal, Juan Jacobo Simón, Bernal, José Joaquín +1
Computer Science · Engineering · #Advanced Wireless Communication Techniques #Coding theory and cryptography #Error Correcting Code Techniques #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.2509.11757
openalex publication_date 2025/09/15 · openalex created_date 2025/10/12 · openalex updated_date 2026/07/28
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.