Hierarchical Locally Recoverable Codes on surfaces

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Carolina Araújo, Luana Costa, Beth Malmskog, Jorge Mello, Eliza Menezes, Cecília Salgado, Lara Vicino
DOI: 10.48550/arxiv.2602.01464
Cited by: 0

Abstract

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.

Fields of Study & Subjects

Coding theory and cryptography Algebraic Geometry and Number Theory Advanced Combinatorial Mathematics

Publication details

Journal / source
arXiv (Cornell University)
Publication date
1 February 2026
Language
EN
Document type
Preprint