Ruled surfaces over finite fields, and some codes over them
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909802160979968 |
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| author | Blache, Régis Hallouin, Emmanuel |
| author_facet | Blache, Régis Hallouin, Emmanuel |
| contents | In the first part of this article, we consider ruled surfaces defined over a finite field; we introduce invariants for them, and describe some explicit contructions that illustrate possible behaviour of these invariants. In the second part, we consider evaluation codes on some such surfaces; we first estimate their parameters, then we construct asymptotically good families of such codes, and we show that their asymptotic parameters are better than the ones of the corresponding product codes. We also consider local properties of these codes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18698 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ruled surfaces over finite fields, and some codes over them Blache, Régis Hallouin, Emmanuel Information Theory Algebraic Geometry Number Theory In the first part of this article, we consider ruled surfaces defined over a finite field; we introduce invariants for them, and describe some explicit contructions that illustrate possible behaviour of these invariants. In the second part, we consider evaluation codes on some such surfaces; we first estimate their parameters, then we construct asymptotically good families of such codes, and we show that their asymptotic parameters are better than the ones of the corresponding product codes. We also consider local properties of these codes. |
| title | Ruled surfaces over finite fields, and some codes over them |
| topic | Information Theory Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2509.18698 |