Gauss-Dickson Codes
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909847573757952 |
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| author | Katre, Shashikant. A. Jadhav, Vikas S. |
| author_facet | Katre, Shashikant. A. Jadhav, Vikas S. |
| contents | Let l be an odd prime. For primes, p \equiv 1 (mod l), Gauss (l = 3) and Dickson (l = 5) considered the Diophantine systems in terms of which cyclotomic numbers of order 3 and 5 were obtained. The aim of this paper is to show how to obtain 1-error detecting [2, 1, 2] code and 1-error correcting [4, 2, 3] code in terms of the solutions of these diophantine systems in the set up of finite fields of q = p^α elements, p \equiv 1 (mod l), l = 3, 5 |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_13376 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gauss-Dickson Codes Katre, Shashikant. A. Jadhav, Vikas S. Number Theory Primary: 11T24, 11T71, 11R18. Secondary: 11T22 Let l be an odd prime. For primes, p \equiv 1 (mod l), Gauss (l = 3) and Dickson (l = 5) considered the Diophantine systems in terms of which cyclotomic numbers of order 3 and 5 were obtained. The aim of this paper is to show how to obtain 1-error detecting [2, 1, 2] code and 1-error correcting [4, 2, 3] code in terms of the solutions of these diophantine systems in the set up of finite fields of q = p^α elements, p \equiv 1 (mod l), l = 3, 5 |
| title | Gauss-Dickson Codes |
| topic | Number Theory Primary: 11T24, 11T71, 11R18. Secondary: 11T22 |
| url | https://arxiv.org/abs/2510.13376 |