Permutation polynomials of degree 6 or 7 over finite fields of characteristic 2

被引：24

作者：

Li, Jiyou ^{[2
]}

Chandler, David B. ^{[1
]}

Xiang, Qing ^{[1
]}

机构：

[1] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

[2] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2010年 / 16卷 / 06期

关键词：

Finite field; Multinomial coefficient; Permutation polynomial; ELEMENTS;

D O I：

10.1016/j.ffa.2010.07.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In Dickson (1896-1897) [2], the author listed all permutation polynomials up to degree 5 over an arbitrary finite field, and all permutation polynomials of degree 6 over finite fields of odd characteristic. The classification of degree 6 permutation polynomials over finite fields of characteristic 2 was left incomplete. In this paper we complete the classification of permutation polynomials of degree 6 over finite fields of characteristic 2. In addition, all permutation polynomials of degree 7 over finite fields of characteristic 2 are classified. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：406 / 419

页数：14

共 50 条

[1] Permutation polynomials of degree 8 over finite fields of characteristic 2
Fan, Xiang
FINITE FIELDS AND THEIR APPLICATIONS, 2020, 64
[2] A classification of permutation polynomials of degree 7 over finite fields
Fan, Xiang
FINITE FIELDS AND THEIR APPLICATIONS, 2019, 59 : 1 - 21
[3] On permutation polynomials over finite fields of characteristic 2
Gupta, Rohit
Sharma, R. K.
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2016, 15 (07)
[4] PERMUTATION POLYNOMIALS OF DEGREE 8 OVER FINITE FIELDS OF ODD CHARACTERISTIC
Fan, Xiang
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2020, 101 (01) : 40 - 55
[5] Enumerating permutation polynomials over finite fields by degree
Konyagin, S
Pappalardi, F
FINITE FIELDS AND THEIR APPLICATIONS, 2002, 8 (04) : 548 - 553
[6] Complete permutation polynomials over finite fields of odd characteristic
Xu Guangkui
Cao, Xiwang
FINITE FIELDS AND THEIR APPLICATIONS, 2015, 31 : 228 - 240
[7] On Inverses of Permutation Polynomials of Small Degree Over Finite Fields
Zheng, Yanbin
Wang, Qiang
Wei, Wenhong
IEEE TRANSACTIONS ON INFORMATION THEORY, 2020, 66 (02) : 914 - 922
[8] Enumerating permutation polynomials over finite fields by degree II
Konyagin, Sergei
Pappalardi, Francesco
Finite Fields Appl., 1 (26-37):
[9] Enumerating permutation polynomials over finite fields by degree II
Konyagin, S
Pappalardi, F
FINITE FIELDS AND THEIR APPLICATIONS, 2006, 12 (01) : 26 - 37
[10] On constructing complete permutation polynomials over finite fields of even characteristic
Wu, Baofeng
Lin, Dongdai
DISCRETE APPLIED MATHEMATICS, 2015, 184 : 213 - 222

← 1 2 3 4 5 →