New classes of permutation trinomials over Fq3

被引：12

作者：

Gupta, Rohit ^{[1
]}

Gahlyan, Pooja ^{[2
]}

Sharma, R. K. ^{[2
]}

机构：

[1] Birla Inst Technol & Sci Pilani, Dept Math, Hyderabad Campus, Hyderabad 500078, Telangana, India

[2] IIT Delhi, Dept Math, New Delhi 110016, India

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2022年 / 84卷

关键词：

Finite field; Permutation polynomial; Linearized polynomial; AB function; APN function; EA-equivalence; FINITE-FIELDS; POLYNOMIALS; BINOMIALS;

D O I：

10.1016/j.ffa.2022.102110

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we propose three new classes of permutation trinomials over Fq3. The first two classes are of the form x + L(xq2+q-1), where L(x) is an element of {x + Axq, x + Axq2 }, q even, and the third class is x + Axq2-q +1 + A2xq2 , q odd. In fact we prove a conjecture proposed by Gong, Gao and Liu [8] about permutation trinomials of the form xq +1 + L(x) is an element of Fq3 [x] as a particular case of our results. Moreover, we determine necessary and sufficient conditions for the permutation trinomials studied. We also show that the permutation trinomials proposed in this paper are new in the sense that they are not quasi-multiplicative equivalent to permutation trinomials over Fq3 known so far. (c) 2022 Elsevier Inc. All rights reserved.

引用

页数：21

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