On the existence of quaternary Hermitian LCD codes with Hermitian dual distance 1

Abstract

For k≥2 and a positive integer d0, we show that if there exists no quaternary Hermitian linear complementary dual [n,k,d] code with d≥d0 and Hermitian dual distance greater than or equal to 2, then there exists no quaternary Hermitian linear complementary dual [n,k,d] code with d≥d0 and Hermitian dual distance 1. As a consequence, we generalize a result by Araya, Harada and Saito on the nonexistence of some quaternary Hermitian linear complementary dual codes.