On generator polynomial matrices of quasi-cyclic codes with linear complementary duals

Norifumi    Ojiro; Hajime  Matsui

doi:10.13069/jacodesmath.v12i3.324

Norifumi Ojiro Toyota Technological Institute
Hajime Matsui Toyota Technological Institute

DOI: https://doi.org/10.13069/jacodesmath.v12i3.324

Keywords: LCD code, Quasi-cyclic code, Reversible code, Optimal code, Generator polynomial matrix

Abstract

Using notion of generator polynomial matrices of quasi-cyclic codes, we show a necessary and sufficient condition for which these codes are to be linear complementary dual. This extends the well-known result by Yang and Massey on cyclic codes to quasi-cyclic codes. As an application we present various examples of optimal binary LCD quasi-cyclic codes.