Application of the Cartier operator in coding theory

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2024-03-29 DOI:10.1016/j.ffa.2024.102419

Vahid Nourozi

引用次数: 0

Abstract

The a-number is an invariant of the isomorphism class of the p-torsion group scheme. We use the Cartier operator on $H^{0} (A_{2}, Ω^{1})$ to find a closed formula for the a-number of the form $A_{2} = v (Y^{\sqrt{q}} + Y - x^{\frac{\sqrt{q} + 1}{2}})$ where $q = p^{s}$ over the finite field $F_{q^{2}}$ . The application of the computed a-number in coding theory is illustrated by the relationship between the algebraic properties of the curve and the parameters of codes that are supported by it.

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卡蒂埃算子在编码理论中的应用

a 数是 p 扭转群方案同构类的不变式。我们利用 H0(A2,Ω1)上的卡蒂埃算子，找到了有限域 Fq2 上 q=ps 的 A2=v(Yq+Y-xq+12) 形式的 a 数封闭公式。曲线的代数特性与曲线支持的编码参数之间的关系，说明了计算出的 a 数在编码理论中的应用。

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.