Involutions of finite abelian groups with explicit constructions on finite fields

IF 1.4 2区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS Designs, Codes and Cryptography Pub Date : 2024-08-12 DOI:10.1007/s10623-024-01474-y

Ruikai Chen, Sihem Mesnager

引用次数: 0

Abstract

In this paper, we study properties and constructions of a general family of involutions of finite abelian groups, especially those of finite fields. The involutions we are interested in have the form \(\lambda +g\circ \tau \), where \(\lambda \) and \(\tau \) are endomorphisms of a finite abelian group and g is an arbitrary map on this group. We present some involutions explicitly written as polynomials for the special cases of multiplicative and additive groups of finite fields.

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有限无边群的卷积与有限域上的显式构造

在本文中，我们将研究有限无边群，尤其是有限域的无边群的一般渐开线族的性质和构造。我们感兴趣的渐开线具有 \(\lambda +g\circ \tau \)的形式，其中 \(\lambda \)和 \(\tau \)是有限无边际群的内变形，g是这个群上的任意映射。对于有限域的乘法群和加法群的特殊情况，我们提出了一些明确写成多项式的渐开线。

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

Designs, Codes and Cryptography 工程技术-计算机：理论方法

CiteScore

2.80

自引率

12.50%

发文量

157

审稿时长

16.5 months

期刊介绍： Designs, Codes and Cryptography is an archival peer-reviewed technical journal publishing original research papers in the designated areas. There is a great deal of activity in design theory, coding theory and cryptography, including a substantial amount of research which brings together more than one of the subjects. While many journals exist for each of the individual areas, few encourage the interaction of the disciplines. The journal was founded to meet the needs of mathematicians, engineers and computer scientists working in these areas, whose interests extend beyond the bounds of any one of the individual disciplines. The journal provides a forum for high quality research in its three areas, with papers touching more than one of the areas especially welcome. The journal also considers high quality submissions in the closely related areas of finite fields and finite geometries, which provide important tools for both the construction and the actual application of designs, codes and cryptographic systems. In particular, it includes (mostly theoretical) papers on computational aspects of finite fields. It also considers topics in sequence design, which frequently admit equivalent formulations in the journal’s main areas. Designs, Codes and Cryptography is mathematically oriented, emphasizing the algebraic and geometric aspects of the areas it covers. The journal considers high quality papers of both a theoretical and a practical nature, provided they contain a substantial amount of mathematics.