The automorphism groups of a maximal function field with the second largest genus and its algebraic geometry 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_ | 1866912730564263936 |
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| author | Hu, Xubin Ma, Liming |
| author_facet | Hu, Xubin Ma, Liming |
| contents | In this manuscript, we investigate the automorphism group of a maximal function field with the second largest possible genus over finite field of even characteristic, which is called the Abdón--Torres function field. As an application, we determine the automorphism groups of one-point algebraic geometry codes from such a maximal function field. It turns out that the automorphism groups of one-point algebraic geometry codes agree with that of the Abdón--Torres function field except for the trivial cases. Moreover, we provide a family of maximal function fields with explicit defining equations via considering fixed subfields with respect to some subgroups of automorphism group of the Abdón--Torres function field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21292 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The automorphism groups of a maximal function field with the second largest genus and its algebraic geometry codes Hu, Xubin Ma, Liming Number Theory In this manuscript, we investigate the automorphism group of a maximal function field with the second largest possible genus over finite field of even characteristic, which is called the Abdón--Torres function field. As an application, we determine the automorphism groups of one-point algebraic geometry codes from such a maximal function field. It turns out that the automorphism groups of one-point algebraic geometry codes agree with that of the Abdón--Torres function field except for the trivial cases. Moreover, we provide a family of maximal function fields with explicit defining equations via considering fixed subfields with respect to some subgroups of automorphism group of the Abdón--Torres function field. |
| title | The automorphism groups of a maximal function field with the second largest genus and its algebraic geometry codes |
| topic | Number Theory |
| url | https://arxiv.org/abs/2511.21292 |