Construction and decoding of matrix-product codes from nested codes

Abstract

We consider matrix-product codes $${[C_1\cdots C_s] \cdot A}$$, where $${C_1, \ldots , C_s}$$are nested linear codes and matrix A has full rank. We compute their minimum distance and provide a decoding algorithm when A is a non-singular by columns matrix. The decoding algorithm decodes up to half of the minimum distance.