Self-dual 2-quasi Negacyclic Codes over Finite Fields

Yun Fan; Yue Leng

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arXiv · 2405.13320

Self-dual 2-quasi Negacyclic Codes over Finite Fields

Yun Fan·Yue Leng

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Abstract

In this paper, we investigate the existence and asymptotic property of self-dual $2$-quasi negacyclic codes of length $2n$ over a finite field of cardinality $q$. When $n$ is odd, we show that the $q$-ary self-dual $2$-quasi negacyclic codes exist if and only if $q\,{\not\equiv}-\!1~({\rm mod}~4)$. When $n$ is even, we prove that the $q$-ary self-dual $2$-quasi negacyclic codes always exist. By using the technique introduced in this paper, we prove that $q$-ary self-dual $2$-quasi negacyclic codes are asymptotically good.

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Yun Fan, Yue Leng. 2024-05-22. Self-dual 2-quasi Negacyclic Codes over Finite Fields. https://arxiv.org/abs/2405.13320

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