On the P-construction of algebraic-geometry codes

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2024-06-05 DOI:10.1016/j.ffa.2024.102448

R. Toledano , M. Vides

引用次数: 0

Abstract

We construct algebraic-geometry codes by using projective systems from projective curves over a finite field and the global sections of invertible sheaves on these curves. We also prove a formula for the Hilbert function of a finite set of points in a projective space in terms of the rank of a matrix constructed with the Veronese embedding and we use it to estimate the minimum distance of the dual codes.

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论代数几何代码的 P 构造

我们利用有限域上的投影曲线的投影系统以及这些曲线上的可逆剪切的全局截面来构造代数几何代码。我们还证明了一个投影空间中有限点集的希尔伯特函数公式，该公式与用维罗内嵌入构建的矩阵的秩有关，我们用它来估计对偶码的最小距离。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Finite Fields and Their Applications 数学-数学

CiteScore

2.00

自引率

20.00%

发文量

133

审稿时长

6-12 weeks

期刊介绍： Finite Fields and Their Applications is a peer-reviewed technical journal publishing papers in finite field theory as well as in applications of finite fields. As a result of applications in a wide variety of areas, finite fields are increasingly important in several areas of mathematics, including linear and abstract algebra, number theory and algebraic geometry, as well as in computer science, statistics, information theory, and engineering. For cohesion, and because so many applications rely on various theoretical properties of finite fields, it is essential that there be a core of high-quality papers on theoretical aspects. In addition, since much of the vitality of the area comes from computational problems, the journal publishes papers on computational aspects of finite fields as well as on algorithms and complexity of finite field-related methods. The journal also publishes papers in various applications including, but not limited to, algebraic coding theory, cryptology, combinatorial design theory, pseudorandom number generation, and linear recurring sequences. There are other areas of application to be included, but the important point is that finite fields play a nontrivial role in the theory, application, or algorithm.