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IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2025-06-13 DOI:10.1016/j.ffa.2025.102675

Denis S. Krotov, Ivan Yu. Mogilnykh

引用次数: 0

摘要

非素数阶有限域上的加性一权码等价于射影空间中点的特殊子空间覆盖，我们称之为多重扩展。本文研究了多重扩散参数的表征，它等价于覆盖半径为1的可加性完全正则码的参数表征，并通过对偶性，等价于覆盖半径为1的可加性完全正则码的参数表征。我们对域的素数平方阶情况下的这些参数进行了表征，并对素数立方阶情况和素数四次情况进行了部分表征，包括对8阶、27阶和16阶的完整表征。

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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Multispreads

Additive one-weight codes over a finite field of non-prime order are equivalent to special subspace coverings of the points of a projective space, which we call multispreads. The current paper is devoted to the characterization of the parameters of multispreads, which is equivalent to the characterization of the parameters of additive one-weight codes and, via duality, of additive completely regular codes of covering radius 1 (intriguing sets). We characterize these parameters for the case of the prime-square order of the field and make a partial characterization for the prime-cube case and the case of the fourth degree of a prime, including a complete characterization for orders 8, 27, and 16.

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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.