Hierarchical Locally Recoverable Codes on surfaces
Fuente:
arXiv
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| Autori principali: | , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866910008351916032 |
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| author | Araujo, Carolina Costa, Luana Malmskog, Beth Mello, Jorge Menezes, Eliza Salgado, Cecília Vicino, Lara |
| author_facet | Araujo, Carolina Costa, Luana Malmskog, Beth Mello, Jorge Menezes, Eliza Salgado, Cecília Vicino, Lara |
| contents | We construct locally recoverable codes with hierarchy from surfaces in $\mathbb{A}^3$ admitting a fibration by curves of Artin-Schreier or Kummer type. We derive the parameters of our codes by leveraging the geometry and arithmetic of the fibration, which is obtained by projection onto one of the coordinates. As a byproduct, we obtain estimates for (and in one case an explicit count of) the number of rational points in certain families of surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_01464 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hierarchical Locally Recoverable Codes on surfaces Araujo, Carolina Costa, Luana Malmskog, Beth Mello, Jorge Menezes, Eliza Salgado, Cecília Vicino, Lara Algebraic Geometry Information Theory 11G20, 14G50, 94B27 We construct locally recoverable codes with hierarchy from surfaces in $\mathbb{A}^3$ admitting a fibration by curves of Artin-Schreier or Kummer type. We derive the parameters of our codes by leveraging the geometry and arithmetic of the fibration, which is obtained by projection onto one of the coordinates. As a byproduct, we obtain estimates for (and in one case an explicit count of) the number of rational points in certain families of surfaces. |
| title | Hierarchical Locally Recoverable Codes on surfaces |
| topic | Algebraic Geometry Information Theory 11G20, 14G50, 94B27 |
| url | https://arxiv.org/abs/2602.01464 |