LCD matrix product codes with an application

Abstract

Matrix product (MP) codes over a finite field [Formula: see text], where [Formula: see text] a prime power, were first introduced by Blackmore and Norton [MP codes over [Formula: see text], Appl. Algebra Engrg. Comm. Comput. 12 (2001) 477–500]. This paper investigates linear complementary dual (LCD) MP codes over finite commutative Frobenius rings. We derive a necessary and sufficient condition for an MP code to have an LCD. We provide some efficient constructions of LCD MP codes. Finally, we have shown an application on cryptography of LCD codes.