Nodal surfaces in $\mathbb{P}^3$ and coding theory
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915300748820480 |
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| author | Kurz, Sascha |
| author_facet | Kurz, Sascha |
| contents | To each nodal hypersurface one can associate a binary linear code. Here we show that the binary linear code associated to sextics in $\mathbb{P}^3$ with the maximum number of $65$ nodes, as e.g. the Barth sextic, is unique. We also state possible candidates for codes that might be associated with a hypothetical septic attaining the currently best known upper bound for the maximum number of nodes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_17531 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nodal surfaces in $\mathbb{P}^3$ and coding theory Kurz, Sascha Combinatorics Information Theory Algebraic Geometry 14J70, 94B05 To each nodal hypersurface one can associate a binary linear code. Here we show that the binary linear code associated to sextics in $\mathbb{P}^3$ with the maximum number of $65$ nodes, as e.g. the Barth sextic, is unique. We also state possible candidates for codes that might be associated with a hypothetical septic attaining the currently best known upper bound for the maximum number of nodes. |
| title | Nodal surfaces in $\mathbb{P}^3$ and coding theory |
| topic | Combinatorics Information Theory Algebraic Geometry 14J70, 94B05 |
| url | https://arxiv.org/abs/2505.17531 |