On permutation polynomials of the form x1+2k + L(x)

被引：10

作者：

Gong, Xin ^{[1
,2
]}

Gao, Guangpu ^{[3
,4
]}

Liu, Wenfen ^{[1
,2
]}

机构：

[1] State Key Lab Math Engn & Adv Comp, Zhengzhou 450001, Peoples R China

[2] China Natl Digital Switching Syst Engn & Technol, POB 1001-745, Zhengzhou 450002, Peoples R China

[3] Luoyang Univ Foreign Languages, Dept Language Engn, Luoyang 471003, Henan Province, Peoples R China

[4] Chinese Acad Sci, Inst Informat Engn, State Key Lab Informat Secur, Beijing 100093, Peoples R China

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2016年 / 93卷 / 10期

关键词：

permutation polynomial; linearized polynomial; trace function; finite field; Bentfunction;

D O I：

10.1080/00207160.2015.1072171

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the open problem of Li and Wang [On EA-equivalence of certain permutations to power mappings, Des. Codes Cryptogr. 58(2011), pp. 259-269] that whether the polynomial x(1+2k) + L(x) on GF(2(n)) is a permutation for gcd(k,n) > 1. Several classes of polynomials of the form x(1+2k) + L(x) are proven to be permutations by decomposing the finite field GF(2(n)) when n equivalent to 0 (mod 3). Some relationships among this type of permutation polynomials, which allow certain secondary constructions, are also proposed.

引用

页码：1715 / 1722

页数：8

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