Locally Recoverable Codes with availability from a family of fibered surfaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915661991641088 |
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| author | Salgado, Cecília Vicino, Lara |
| author_facet | Salgado, Cecília Vicino, Lara |
| contents | We construct Locally Recoverable Codes (LRCs) with availability $2$ from a family of fibered surfaces. To obtain the locality and availability properties, and to estimate the minimum distance of the codes, we combine techniques coming from the theory of one-variable function fields and from the theory of fibrations on surfaces. When the locality parameter is $r=3$, we obtain a sharp bound on the minimum distance of the codes. In that case, we give a geometric interpretation of our codes in terms of doubly elliptic surfaces. In particular, this provides the first instance of an error correcting code constructed using a (doubly elliptic) K3 surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08100 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Locally Recoverable Codes with availability from a family of fibered surfaces Salgado, Cecília Vicino, Lara Algebraic Geometry Information Theory 14H05, 14G50, 94B27 We construct Locally Recoverable Codes (LRCs) with availability $2$ from a family of fibered surfaces. To obtain the locality and availability properties, and to estimate the minimum distance of the codes, we combine techniques coming from the theory of one-variable function fields and from the theory of fibrations on surfaces. When the locality parameter is $r=3$, we obtain a sharp bound on the minimum distance of the codes. In that case, we give a geometric interpretation of our codes in terms of doubly elliptic surfaces. In particular, this provides the first instance of an error correcting code constructed using a (doubly elliptic) K3 surface. |
| title | Locally Recoverable Codes with availability from a family of fibered surfaces |
| topic | Algebraic Geometry Information Theory 14H05, 14G50, 94B27 |
| url | https://arxiv.org/abs/2512.08100 |