Matrix product codes over F_p

Abstract

We will present in this paper the concept of matrix-product code [C₁, C₂, ... , C_s]A where C₁, C₂, ... , C_s are linear codes and matrix A has full rank. The purpose of this paper is to give some properties of these codes that will be useful later, the two main points being the existence of a MacWilliams identity (which is one reason the existence of the phenomenon of duality formal) and the structure of the matrix-product code on ℤ_p^k.