Self-dual 2-quasi Negacyclic Codes over Finite Fields
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909208234950656 |
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| author | Fan, Yun Leng, Yue |
| author_facet | Fan, Yun Leng, Yue |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_13320 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Self-dual 2-quasi Negacyclic Codes over Finite Fields Fan, Yun Leng, Yue Information Theory 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. |
| title | Self-dual 2-quasi Negacyclic Codes over Finite Fields |
| topic | Information Theory |
| url | https://arxiv.org/abs/2405.13320 |