Matrix-product codes over finite chain rings

Tim Blackmore and Graham H. Norton introduced the notion of matrix-product codes over finite fields. The present paper provides a generalization to finite chain rings. For codes a distance function is defined using a homogeneous weight function in the ring. It is proved that the minimum distance of a matrix-product codes is determined by the minimum distances of the separate codes. At the end of the paper we focus on Galois rings and define a special family of matrix-product codes.