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.
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页码：437 / 449
页数：13
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