List decoding of matrix-product codes from nested codes: An application to quasi-cyclic codes
Fernando Hernando, Tom Høholdt, Diego Ruano · Advances in Mathematics of Communications · 2012
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.