On a conjecture on permutation rational functions over finite fields

被引：5

作者：

Bartoli, Daniele ^{[1
]}

Hou, Xiang-dong ^{[2
]}

机构：

[1] Univ Perugia, Dipartimento Matemat & Informat, Perugia, Italy

[2] Univ S Florida, Dept Math & Stat, Tampa, FL 33620 USA

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2021年 / 76卷

关键词：

Finite field; Lang-Weil bound; Permutation; Rational function; TRINOMIALS; POLYNOMIALS;

D O I：

10.1016/j.ffa.2021.101904

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let p be a prime and n be a positive integer, and consider f(b)(X) = X +(X-p-X+b)(-1) is an element of F-pn(X), where b is an element of F-pn is such that Tr-pn/p(b) not equal 0. It is known that (i) f(b) permutes F-pn for p = 2, 3 and all n >= 1; (ii) for p > 3 and n = 2, f(b) permutes F-p2 if and only if Tr-p2/p(b) = +/- 1; and (iii) for p > 3 and n > 5, fb does not permute F-pn. It has been conjectured that for p > 3 and n = 3, 4, f(b) does not permute F-pn. We prove this conjecture for sufficiently large p. (C) 2021 Published by Elsevier Inc.

引用

页数：16

共 50 条

[21] An application of the Hasse-Weil bound to rational functions over finite fields [J].

Hou, Xiang-dong ;

Iezzi, Annamaria .

ACTA ARITHMETICA, 2020, 195 (02) :207-216

[22] On a class of permutation rational functions involving trace maps [J].

Chen, Ruikai ;

Mesnager, Sihem .

DESIGNS CODES AND CRYPTOGRAPHY, 2024, 92 (05) :1327-1339

[23] More classes of permutation pentanomials over finite fields with characteristic two [J].

Zhang, Tongliang ;

Zheng, Lijing ;

Zhao, Hanbing .

FINITE FIELDS AND THEIR APPLICATIONS, 2024, 98

[24] Further results on permutation pentanomials over finite fields with characteristic two [J].

Zhang, Tongliang ;

Kan, Haibin ;

Zheng, Lijing ;

Peng, Jie ;

Zhao, Hanbing .

DESIGNS CODES AND CRYPTOGRAPHY, 2025,

[25] Permutation binomials over finite fields [J].

Oliveira, Jose Alves ;

Brochero Martinez, F. E. .

DISCRETE MATHEMATICS, 2022, 345 (03)

[26] Determination of a type of permutation trinomials over finite fields [J].

Hou, Xiang-dong .

ACTA ARITHMETICA, 2014, 166 (03) :253-278

[27] Determination of a type of permutation binomials over finite fields [J].

Hou, Xiang-Dong ;

Lappano, Stephen D. .

JOURNAL OF NUMBER THEORY, 2015, 147 :14-23

[28] A survey of permutation binomials and trinomials over finite fields [J].

Hou, Xiang-dong .

TOPICS IN FINITE FIELDS, 2015, 632 :177-+

[29] The compositional inverses of the permutation polynomials from trace functions over finite fields [J].

Wu, Danyao ;

Yuan, Pingzhi .

DESIGNS CODES AND CRYPTOGRAPHY, 2025,

[30] More classes of permutation hexanomials and pentanomials over finite fields with even characteristic [J].

Zhang, Tongliang ;

Zheng, Lijing ;

Hao, Xinghui .

FINITE FIELDS AND THEIR APPLICATIONS, 2023, 91

← 1 2 3 4 5 →