Several classes of permutation polynomials of the form (xpm - x + δ)s + x over Fp2m

被引：8
|
作者：
Xu, Guangkui [1 ]
Luo, Gaojun [2 ]
Cao, Xiwang [3 ,4 ]
机构：
[1] Huainan Normal Univ, Sch Finance & Math, Huainan 232038, Peoples R China
[2] Nanyang Technol Univ, Sch Phys & Math Sci, 21 Nanyang Link, Singapore 637371, Singapore
[3] Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 210016, Peoples R China
[4] MIIT, Key Lab Math Modeling & High Performance Comp Air, Nanjing 210016, Peoples R China
来源：
FINITE FIELDS AND THEIR APPLICATIONS | 2022年 / 79卷
基金：
中国国家自然科学基金;
关键词：
Finite field; Permutation polynomial; Complete permutation polynomial; Trace function;
D O I：
10.1016/j.ffa.2022.102001
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we give a further study on the permutation behavior of polynomials of a special form by considering the number of solutions of certain equations over finite fields. First, four classes of permutation polynomials of the form (x(2m) + x + delta)(s) + x over F-22m are presented. Notably, some necessary and sufficient conditions for this kind of polynomials to permute F-22m are provided. Second, we present several classes of permutation polynomials of the form (x(pm) - x + delta)(s) + x over F-p2m of odd characteristic, some of which can provide complete permutation polynomials of this form over F-32m. (C) 2022 Elsevier Inc. All rights reserved.
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页数：21
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