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arXiv · 2104.07432

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

Keita Ishizuka·Ken Saito
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Abstract

For $k \ge 2$ and a positive integer $d_0$, we show that if there exists no quaternary Hermitian linear complementary dual $[n,k,d]$ code with $d \ge d_0$ and Hermitian dual distance greater than or equal to $2$, then there exists no quaternary Hermitian linear complementary dual $[n,k,d]$ code with $d \ge d_0$ 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.

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Keita Ishizuka, Ken Saito. 2021-04-15. On the existence of quaternary Hermitian LCD codes with Hermitian dual distance $1$. https://arxiv.org/abs/2104.07432

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