Further results on permutation polynomials of the form (xpm - x plus δ)s + L(x) over Fp2m

被引：19

作者：

Wang, Libo ^{[1
,2
]}

Wu, Baofeng ^{[1
]}

Liu, Zhuojun ^{[2
]}

机构：

[1] Chinese Acad Sci, Inst Informat Engn, SKLOIS, Beijing 100093, Peoples R China

[2] Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2017年 / 44卷

基金：

中国国家自然科学基金;

关键词：

Finite field; Permutation polynomial; Cubic equation; Quadratic equation; FINITE-FIELDS;

D O I：

10.1016/j.ffa.2016.11.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, some classes of permutation polynomials of the form (x(pm) - x + delta)(s) + L(x) over the finite field F-p2m are investigated by determining the number of solutions of certain equations, where L(x) = x or x(pm) + x. More precisely, for an integer s satisfying s(p(m) +1) equivalent to p(m) +1 (mod p(2m) - 1), we give four classes of permutation polynomials of the form (x(2m) + x delta)(s) + x over F-22m, and five classes of permutation polynomials of the form (x(3m) - x + delta)(s) + x(3m) + x over F-32m, respectively. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：92 / 112

页数：21

共 17 条

[1]

[Anonymous], 1997, ENCY MATH APPL

[2] ON SOLUTION OF ALGEBRAIC EQUATIONS OVER FINITE FIELDS [J].

BERLEKAM.ER ;

RUMSEY, H ;

SOLOMON, G .

INFORMATION AND CONTROL, 1967, 10 (06) :553-&

[3] New Kloosterman sums identities over F2m for all m [J].

Helleseth, T ;

Zinoviev, V .

FINITE FIELDS AND THEIR APPLICATIONS, 2003, 9 (02) :187-193

[4] Permutation polynomials over finite fields - A survey of recent advances [J].

Hou, Xiang-dong .

FINITE FIELDS AND THEIR APPLICATIONS, 2015, 32 :82-119

[5] Further results on a class of permutation polynomials over finite fields [J].

Li, Nian ;

Helleseth, Tor ;

Tang, Xiaohu .

FINITE FIELDS AND THEIR APPLICATIONS, 2013, 22 :16-23

[6]

Mullen G.L., 2013, Handbook of Finite Fields

[7] Permutation polynomials of the form (xpm-x plus δ)s+L(x) over the finite field Fp2m of odd characteristic [J].

Tu, Ziran ;

Zeng, Xiangyong ;

Li, Chunlei ;

Helleseth, Tor .

FINITE FIELDS AND THEIR APPLICATIONS, 2015, 34 :20-35

[8] Two classes of permutation polynomials having the form (x2m + x plus δ)S + x [J].

Tu, Ziran ;

Zeng, Xiangyong ;

Jiang, Yupeng .

FINITE FIELDS AND THEIR APPLICATIONS, 2015, 31 :12-24

[9] Permutation polynomials of the form (xP-x+δ)S+L(x) [J].

Yuan, Jin ;

Ding, Cunsheng ;

Wang, Huaxiong ;

Pieprzyk, Josef .

FINITE FIELDS AND THEIR APPLICATIONS, 2008, 14 (02) :482-493

[10] Four classes of permutation polynomials of F2m [J].

Yuan, Jin ;

Ding, Cunsheng .

FINITE FIELDS AND THEIR APPLICATIONS, 2007, 13 (04) :869-876

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