List Decoding of Matrix-Product Codes from nested codes: an application to Quasi-Cyclic codes

Fernando Hernando, Tom Høholdt, Diego Ruano

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    Abstract

    A list decoding algorithm for matrix-product codes is provided when $C_1,..., C_s$ are nested linear codes and $A$ is a non-singular by columns matrix. We estimate the probability of getting more than one codeword as output when the constituent codes are Reed-Solomon codes. We extend this list decoding algorithm for matrix-product codes with polynomial units, which are quasi-cyclic codes. Furthermore, it allows us to consider unique decoding for matrix-product codes with polynomial units.
    Original languageEnglish
    JournalAdvances in Mathematics of Communication
    Volume6
    Issue number3
    Pages (from-to)259-272
    ISSN1930-5346
    DOIs
    Publication statusPublished - 2012

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