Ruled surfaces over finite fields, and some codes over them

Fuente: arXiv
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Main Authors: Blache, Régis, Hallouin, Emmanuel
Format: Preprint
Published: 2025
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author Blache, Régis
Hallouin, Emmanuel
author_facet Blache, Régis
Hallouin, Emmanuel
contents In the first part of this article, we consider ruled surfaces defined over a finite field; we introduce invariants for them, and describe some explicit contructions that illustrate possible behaviour of these invariants. In the second part, we consider evaluation codes on some such surfaces; we first estimate their parameters, then we construct asymptotically good families of such codes, and we show that their asymptotic parameters are better than the ones of the corresponding product codes. We also consider local properties of these codes.
format Preprint
id arxiv_https___arxiv_org_abs_2509_18698
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Ruled surfaces over finite fields, and some codes over them
Blache, Régis
Hallouin, Emmanuel
Information Theory
Algebraic Geometry
Number Theory
In the first part of this article, we consider ruled surfaces defined over a finite field; we introduce invariants for them, and describe some explicit contructions that illustrate possible behaviour of these invariants. In the second part, we consider evaluation codes on some such surfaces; we first estimate their parameters, then we construct asymptotically good families of such codes, and we show that their asymptotic parameters are better than the ones of the corresponding product codes. We also consider local properties of these codes.
title Ruled surfaces over finite fields, and some codes over them
topic Information Theory
Algebraic Geometry
Number Theory
url https://arxiv.org/abs/2509.18698