More permutation polynomials with Niho exponents which permute Fq2

被引：7
作者：
Cao, Xiwang [1 ,2 ]
Hou, Xiang-Dong [3 ]
Mi, Jiafu [1 ]
Xu, Shanding [1 ,4 ]
机构：
[1] Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 210016, Peoples R China
[2] Chinese Acad Sci, Inst Informat Engn, State Key Lab Informat Secur, Beijing 100093, Peoples R China
[3] Univ S Florida, Dept Math & Stat, Tampa, FL 33620 USA
[4] Nanjing Inst Technol, Dept Math & Phys, Nanjing 211167, Peoples R China
来源：
FINITE FIELDS AND THEIR APPLICATIONS | 2020年 / 62卷
关键词：
Permutation polynomial; Trinomial; Niho exponent; Finite field; FINITE-FIELDS; TRINOMIALS;
D O I：
10.1016/j.ffa.2019.101626
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Constructions of permutation polynomials over finite fields have attracted much interests in recent years, especially those with few terms, such as trinomials, due to their simple form and additional properties. In this paper, we construct several classes of permutation trinomials over F-p2k with Niho exponents of the form f(x) = x + lambda(1)x(s(pk-1)+1) + lambda(2)x(t(pk -1)+1); some necessary and sufficient conditions for the polynomial f(x) to permute F-p2k are provided. Specifically, for p = 5, new permutation trinomials are presented. We also give recursive constructions of permutation polynomials using self-reciprocal polynomials. (C) 2019 Elsevier Inc. All rights reserved.
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页数：30
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