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

A list decoding algorithm for matrix-product codes is provided when C1, . . . , Cs 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 unit