Self-dual 2-quasi Negacyclic Codes over Finite Fields
<|reference_start|>Self-dual 2-quasi Negacyclic Codes over Finite Fields: 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.<|reference_end|>
@article{fan2024self-dual,
    title={Self-dual 2-quasi Negacyclic Codes over Finite Fields},
    author={Yun Fan, Yue Leng},
    journal={arXiv preprint arXiv:2405.13320},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.13320},
    primaryClass={cs.IT math.IT}
}