A Deterministic Dimension Property of Twisted Goppa Codes
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866909908881899520 |
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| author | Wang, Kai |
| author_facet | Wang, Kai |
| contents | This paper presents a large-scale computational study on the dimensional properties of twisted Goppa codes. Through the systematic analysis of over 50,000 parameter sets, we uncover a remarkable deterministic regularity: the actual dimension k of a twisted Goppa code is uniquely determined by a set of macro-parameters (q,m,t,b,u). Specifically, when the order of the finite field q, the extension degree m, the degree t of the Goppa polynomial, the translation parameter b of the automorphism, and the order u of the transformation are fixed, the dimension k of the generated code remains constant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13601 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Deterministic Dimension Property of Twisted Goppa Codes Wang, Kai Information Theory This paper presents a large-scale computational study on the dimensional properties of twisted Goppa codes. Through the systematic analysis of over 50,000 parameter sets, we uncover a remarkable deterministic regularity: the actual dimension k of a twisted Goppa code is uniquely determined by a set of macro-parameters (q,m,t,b,u). Specifically, when the order of the finite field q, the extension degree m, the degree t of the Goppa polynomial, the translation parameter b of the automorphism, and the order u of the transformation are fixed, the dimension k of the generated code remains constant. |
| title | A Deterministic Dimension Property of Twisted Goppa Codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2511.13601 |