Hierarchical Locally Recoverable Codes on surfaces

Carolina Araujo; Luana Costa; Beth Malmskog; Jorge Mello; Eliza Menezes; Cecília Salgado Guimarães da Silva; Lara Vicino

doi:10.48550/arXiv.2602.01464

Hierarchical Locally Recoverable Codes on surfaces

Carolina Araujo
, Luana Costa
, Beth Malmskog
, Jorge Mello
, Eliza Menezes
, Cecília Salgado Guimarães da Silva
, Lara Vicino

Algebra

Research output: Working paper › Preprint › Academic

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Abstract

We construct locally recoverable codes with hierarchy from surfaces in A3 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.

Original language	English
Publisher	arXiv
Number of pages	21
DOIs	https://doi.org/10.48550/arXiv.2602.01464
Publication status	Submitted - 1-Feb-2026

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title = "Hierarchical Locally Recoverable Codes on surfaces",

abstract = "We construct locally recoverable codes with hierarchy from surfaces in A3 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.",

author = "Carolina Araujo and Luana Costa and Beth Malmskog and Jorge Mello and Eliza Menezes and \{Salgado Guimar{\~a}es da Silva\}, Cec{\'i}lia and Lara Vicino",

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T1 - Hierarchical Locally Recoverable Codes on surfaces

AU - Araujo, Carolina

AU - Costa, Luana

AU - Malmskog, Beth

AU - Mello, Jorge

AU - Menezes, Eliza

AU - Salgado Guimarães da Silva, Cecília

AU - Vicino, Lara

PY - 2026/2/1

Y1 - 2026/2/1

N2 - We construct locally recoverable codes with hierarchy from surfaces in A3 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.

AB - We construct locally recoverable codes with hierarchy from surfaces in A3 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.

U2 - 10.48550/arXiv.2602.01464

DO - 10.48550/arXiv.2602.01464

M3 - Preprint

BT - Hierarchical Locally Recoverable Codes on surfaces

PB - arXiv

ER -

Hierarchical Locally Recoverable Codes on surfaces

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