Four classes of optimal p-ary cyclic codes
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914172511453184 |
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| author | Fan, Jinmei Feng, Jingyao Men, Yuhan Zhang, Yanhai |
| author_facet | Fan, Jinmei Feng, Jingyao Men, Yuhan Zhang, Yanhai |
| contents | Let p>3 be an odd prime and m be a positive integer. Little progress on the study of optimal p-ary cyclic codes with parameters [p^m-1,p^m-2m-2,4] has been made.In this paper, by weakening the necessary and sufficient conditions on cyclic codes to have codewords of Hamming weight 3 and analyzing the solutions of certain equations over finite fields, four classes of optimal p-ary cyclic codes deduced by p^m+1/2 with parameters [p^m-1,p^m-2m-2,4] are presented.Wherein three classes of optimal p-ary cyclic codes are infinite.Many classes of known optimal quinary cyclic codes with parameters [5^m-1,5^m-2m-2,4] are special cases of the codes constructed in this paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22086 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Four classes of optimal p-ary cyclic codes Fan, Jinmei Feng, Jingyao Men, Yuhan Zhang, Yanhai Information Theory Let p>3 be an odd prime and m be a positive integer. Little progress on the study of optimal p-ary cyclic codes with parameters [p^m-1,p^m-2m-2,4] has been made.In this paper, by weakening the necessary and sufficient conditions on cyclic codes to have codewords of Hamming weight 3 and analyzing the solutions of certain equations over finite fields, four classes of optimal p-ary cyclic codes deduced by p^m+1/2 with parameters [p^m-1,p^m-2m-2,4] are presented.Wherein three classes of optimal p-ary cyclic codes are infinite.Many classes of known optimal quinary cyclic codes with parameters [5^m-1,5^m-2m-2,4] are special cases of the codes constructed in this paper. |
| title | Four classes of optimal p-ary cyclic codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2511.22086 |