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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.16343 |
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| _version_ | 1866916586327113728 |
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| author | Wang, Puyin Luo, Jinquan |
| author_facet | Wang, Puyin Luo, Jinquan |
| contents | In the field of algebraic geometric codes (AG codes), the characterization of dual codes has long been a challenging problem which relies on differentials. In this paper, we provide some descriptions for certain differentials utilizing algebraic structure of finite fields and geometric properties of algebraic curves. Moreover, we construct self-orthogonal and self-dual codes with parameters $[n, k, d]_{q^2}$ satisfying $k + d$ is close to $n$. Additionally, quantum codes with large minimum distance are also constructed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_16343 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Self-orthogonal and self-dual codes from maximal curves Wang, Puyin Luo, Jinquan Information Theory Algebraic Geometry 94B27 In the field of algebraic geometric codes (AG codes), the characterization of dual codes has long been a challenging problem which relies on differentials. In this paper, we provide some descriptions for certain differentials utilizing algebraic structure of finite fields and geometric properties of algebraic curves. Moreover, we construct self-orthogonal and self-dual codes with parameters $[n, k, d]_{q^2}$ satisfying $k + d$ is close to $n$. Additionally, quantum codes with large minimum distance are also constructed. |
| title | Self-orthogonal and self-dual codes from maximal curves |
| topic | Information Theory Algebraic Geometry 94B27 |
| url | https://arxiv.org/abs/2501.16343 |