几类新的有限域上的n-cycle置换  

Some New Classes of ncycle Permutations over Finite Fields

作　　者：张志林 袁平之[1] Zhang Zhilin;Yuan Pingzhi(School of Mathematical Science,South China Normal University,Guangzhou 510640,China)

机构地区：[1]华南师范大学数学科学学院,广州510640

出　　处：《数学理论与应用》2023年第2期32-47,共16页Mathematical Theory and Applications

基　　金：supported by National Natural Science Foundation of China(Nos.12001204,12171163)。

摘　　要：本文给出几类新的有限域上的n-cycle置换.首先,我们给出一个判断Dickson多项式是否为n-cycle置换的方法.其次,我们给出一个线性多项式是否为对合的充要条件.最后,我们给出几类新的不同型的n-cycle置换.This paper presents some new classes of ncycle permutations over finite fields.At first,we present a concise criterion for Dickson polynomials over finite fields being ncycle permutations.Then,we give a necessary and sufficient condition for linearized polynomials over finite fields being involutions.Finally,some interesting new classes of ncycle permutations are demonstrated by considering polynomials of different forms.

关 键 词：n-cycle置换 置换多项式 线性译码 Dickson多项式 线性多项式 有限域 分段函数 

分 类 号：O174.14[理学—数学]