New results on permutation polynomials over finite fields

被引：7
|
作者：
Qin, Xiaoer [1 ,2 ]
Qian, Guoyou [1 ]
Hong, Shaofang [1 ]
机构：
[1] Sichuan Univ, Math Coll, Chengdu 610064, Peoples R China
[2] Yangtze Normal Univ, Coll Math & Comp Sci, Chongqing 408100, Peoples R China
来源：
INTERNATIONAL JOURNAL OF NUMBER THEORY | 2015年 / 11卷 / 02期
基金：
美国国家科学基金会;
关键词：
Permutation polynomial; linearized polynomial; linear translator; matrix; BINOMIALS;
D O I：
10.1142/S1793042115500220
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we get several new results on permutation polynomials over finite fields. First, by using the linear translator, we construct permutation polynomials of the forms L(x) + Sigma(k)(j)(= 1) gamma(j)h(j)(f(j) (x)) and x + Sigma(k)(j)(= 1) gamma(j)f(j) (x). These forms generalize the results obtained by Kyureghyan in 2011. Consequently, we characterize permutation polynomials of the form L(x) + Sigma(l)(i)(= 1) gamma iTrFqm/F-q (h(i)(x)), which extends a theorem of Charpin and Kyureghyan obtained in 2009.
引用
收藏
页码：437 / 449
页数：13
相关论文
共 50 条
  • [1] Some new results on permutation polynomials over finite fields
    Ma, Jingxue
    Zhang, Tao
    Feng, Tao
    Ge, Gennian
    DESIGNS CODES AND CRYPTOGRAPHY, 2017, 83 (02) : 425 - 443
  • [2] Some new results on permutation polynomials over finite fields
    Jingxue Ma
    Tao Zhang
    Tao Feng
    Gennian Ge
    Designs, Codes and Cryptography, 2017, 83 : 425 - 443
  • [3] Further results on permutation polynomials and complete permutation polynomials over finite fields
    Liu, Qian
    Xie, Jianrui
    Liu, Ximeng
    Zou, Jian
    AIMS MATHEMATICS, 2021, 6 (12): : 13503 - 13514
  • [4] Further results on permutation polynomials over finite fields
    Yuan, Pingzhi
    Ding, Cunsheng
    FINITE FIELDS AND THEIR APPLICATIONS, 2014, 27 : 88 - 103
  • [5] A new approach to permutation polynomials over finite fields
    Hou, Xiang-Dong
    FINITE FIELDS AND THEIR APPLICATIONS, 2012, 18 (03) : 492 - 521
  • [6] Further results on a class of permutation polynomials over finite fields
    Li, Nian
    Helleseth, Tor
    Tang, Xiaohu
    FINITE FIELDS AND THEIR APPLICATIONS, 2013, 22 : 16 - 23
  • [7] Permutation Polynomials over Finite Fields
    万大庆
    Acta Mathematica Sinica, 1987, (01) : 1 - 5
  • [8] Permutation Polynomials over Finite Fields
    万大庆
    Acta Mathematica Sinica,English Series, 1987, (01) : 1 - 5
  • [9] New Permutation Reversed Dickson Polynomials over Finite Fields
    Cheng, Kaimin
    ALGEBRA COLLOQUIUM, 2023, 30 (01) : 111 - 120
  • [10] A new approach to permutation polynomials over finite fields, II
    Fernando, Neranga
    Hou, Xiang-dong
    Lappano, Stephen D.
    FINITE FIELDS AND THEIR APPLICATIONS, 2013, 22 : 122 - 158
12345