Hierarchical Locally Recoverable Codes on surfaces
Algebraic Geometry
2026-02-03 v1 Information Theory
math.IT
Abstract
We construct locally recoverable codes with hierarchy from surfaces in 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.
Keywords
Cite
@article{arxiv.2602.01464,
title = {Hierarchical Locally Recoverable Codes on surfaces},
author = {Carolina Araujo and Luana Costa and Beth Malmskog and Jorge Mello and Eliza Menezes and Cecília Salgado and Lara Vicino},
journal= {arXiv preprint arXiv:2602.01464},
year = {2026}
}