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

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.

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