Several new classes of optimal p-ary cyclic codes
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911151231598592 |
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| author | Fang, Mengen Li, Lanqiang Tian, Fuyin Liu, Li |
| author_facet | Fang, Mengen Li, Lanqiang Tian, Fuyin Liu, Li |
| contents | Cyclic codes, as a crucial subclass of linear codes, exhibit broad applications in communication systems, data storage systems, and consumer electronics, primarily attributed to their well-structured algebraic properties. Let $p$ denote an odd prime with $p\geq5$, and let $m$ be a positive integer. The primary objective of this paper is to construct three novel classes of optimal $p$-ary cyclic codes, denoted as ${\mathcal{C}_p}(0,s,t)$, which possess the parameters $[{p^m} - 1,{p^m} - 2m - 2,4]$. Here, $s$ is defined as $s = \frac{{{p^m}+1}}{2}$, and $t$ satisfies the condition $2 \le t \le {p^m} - 2$. Notably, one of the constructed classes includes certain known optimal quinary cyclic codes as special cases. Furthermore, for the specific case when $p=5$, this paper additionally presents four new classes of optimal cyclic codes ${\mathcal{C}_5}(0,s,t)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_09951 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Several new classes of optimal p-ary cyclic codes Fang, Mengen Li, Lanqiang Tian, Fuyin Liu, Li Information Theory Cyclic codes, as a crucial subclass of linear codes, exhibit broad applications in communication systems, data storage systems, and consumer electronics, primarily attributed to their well-structured algebraic properties. Let $p$ denote an odd prime with $p\geq5$, and let $m$ be a positive integer. The primary objective of this paper is to construct three novel classes of optimal $p$-ary cyclic codes, denoted as ${\mathcal{C}_p}(0,s,t)$, which possess the parameters $[{p^m} - 1,{p^m} - 2m - 2,4]$. Here, $s$ is defined as $s = \frac{{{p^m}+1}}{2}$, and $t$ satisfies the condition $2 \le t \le {p^m} - 2$. Notably, one of the constructed classes includes certain known optimal quinary cyclic codes as special cases. Furthermore, for the specific case when $p=5$, this paper additionally presents four new classes of optimal cyclic codes ${\mathcal{C}_5}(0,s,t)$. |
| title | Several new classes of optimal p-ary cyclic codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2509.09951 |