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

04/15/2021

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by   Keita Ishizuka, et al.

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For k ≥ 2 and a positive integer d_0, we show that if there exists no quaternary Hermitian linear complementary dual [n,k,d] code with d ≥ d_0 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 ≥ d_0 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.