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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2405.18023 |
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| _version_ | 1866911891144572928 |
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| author | Jia, Xue Li, Fengwei Sun, Huan Yue, Qin |
| author_facet | Jia, Xue Li, Fengwei Sun, Huan Yue, Qin |
| contents | Classical Goppa codes are a well-known class of codes with applications in code-based cryptography, which are a special case of alternant codes. Many papers are devoted to the search for Goppa codes with a cyclic extension or with a cyclic parity-check subcode. Let $\Bbb F_q$ be a finite field with $q=2^l$ elements, where $l$ is a positive integer. In this paper, we determine all the generator polynomials of cyclic expurgated or extended Goppa codes under some prescribed permutations induced by the projective general linear automorphism $A \in PGL_2(\Bbb F_q)$. Moreover, we provide some examples to support our findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_18023 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generator polynomials of cyclic expurgated or extended Goppa codes Jia, Xue Li, Fengwei Sun, Huan Yue, Qin Information Theory Classical Goppa codes are a well-known class of codes with applications in code-based cryptography, which are a special case of alternant codes. Many papers are devoted to the search for Goppa codes with a cyclic extension or with a cyclic parity-check subcode. Let $\Bbb F_q$ be a finite field with $q=2^l$ elements, where $l$ is a positive integer. In this paper, we determine all the generator polynomials of cyclic expurgated or extended Goppa codes under some prescribed permutations induced by the projective general linear automorphism $A \in PGL_2(\Bbb F_q)$. Moreover, we provide some examples to support our findings. |
| title | Generator polynomials of cyclic expurgated or extended Goppa codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2405.18023 |