New Permutation Reversed Dickson Polynomials over Finite Fields

IF 0.4 4区数学 Q4 MATHEMATICS

Algebra Colloquium Pub Date : 2022-03-20 DOI:10.1142/s1005386723000093

K. Cheng

引用次数: 0

Abstract

Let [Formula: see text] be an odd prime, and [Formula: see text], [Formula: see text] be nonnegative integers. Let [Formula: see text] be the reversed Dickson polynomial of the [Formula: see text]-th kind. In this paper, by using Hermite's criterion, we study the permutational properties of the reversed Dickson polynomials [Formula: see text] over finite fields in the case of [Formula: see text] with [Formula: see text]. In particular, we provide some precise characterizations for [Formula: see text] being permutation polynomials over finite fields with characteristic [Formula: see text] when [Formula: see text], or [Formula: see text], or [Formula: see text].

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有限域上的新置换逆Dickson多项式

设[公式:见文]为奇素数，[公式:见文]，[公式:见文]为非负整数。设[公式:见文]为[公式:见文]-第一类的反Dickson多项式。本文利用Hermite判据，研究了有限域上[公式:见文]与[公式:见文]在[公式:见文]情况下的反向Dickson多项式[公式:见文]的置换性质。特别地，我们提供了[公式:见文]在[公式:见文]，或[公式:见文]，或[公式:见文]时作为有限域上具有特征[公式:见文]的置换多项式的一些精确表征。

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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来源期刊

Algebra Colloquium 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

625

审稿时长

15.6 months

期刊介绍： Algebra Colloquium is an international mathematical journal founded at the beginning of 1994. It is edited by the Academy of Mathematics & Systems Science, Chinese Academy of Sciences, jointly with Suzhou University, and published quarterly in English in every March, June, September and December. Algebra Colloquium carries original research articles of high level in the field of pure and applied algebra. Papers from related areas which have applications to algebra are also considered for publication. This journal aims to reflect the latest developments in algebra and promote international academic exchanges.