Several classes of complete permutation polynomials with Niho exponents

2021 ◽  
Vol 72 ◽  
pp. 101831
Author(s):  
Lisha Li ◽  
Qiang Wang ◽  
Yunge Xu ◽  
Xiangyong Zeng
Keyword(s):  
Permutation Polynomials ◽  
Niho Exponents ◽  
Complete Permutation Polynomials

Several classes of permutation trinomials from Niho exponents over finite fields of characteristic 3

2019 ◽  
Vol 18 (04) ◽  
pp. 1950069
Author(s):  
Qian Liu ◽  
Yujuan Sun
Keyword(s):  
Positive Integer ◽  
Finite Field ◽  
Coding Theory ◽  
Permutation Polynomials ◽  
Combinatorial Designs ◽  
Dickson Polynomial ◽  
Niho Exponents ◽  
Characteristic 3 ◽  
Permutation Trinomials ◽  
Algebraic Forms

Permutation polynomials have important applications in cryptography, coding theory, combinatorial designs, and other areas of mathematics and engineering. Finding new classes of permutation polynomials is therefore an interesting subject of study. Permutation trinomials attract people’s interest due to their simple algebraic forms and additional extraordinary properties. In this paper, based on a seventh-degree and a fifth-degree Dickson polynomial over the finite field [Formula: see text], two conjectures on permutation trinomials over [Formula: see text] presented recently by Li–Qu–Li–Fu are partially settled, where [Formula: see text] is a positive integer.

Constructions of complete permutation polynomials

2018 ◽  
Vol 86 (12) ◽  
pp. 2869-2892 ◽  
Author(s):  
Xiaofang Xu ◽  
Chunlei Li ◽  
Xiangyong Zeng ◽  
Tor Helleseth
Keyword(s):  
Permutation Polynomials ◽  
Complete Permutation Polynomials

A specific type of permutation and complete permutation polynomials over finite fields

2019 ◽  
Vol 19 (04) ◽  
pp. 2050067
Author(s):  
Pınar Ongan ◽  
Burcu Gülmez Temür
Keyword(s):  
Finite Fields ◽  
Permutation Polynomials ◽  
Polynomials Over Finite Fields ◽  
Complete Permutation Polynomials

In this paper, we study polynomials of the form [Formula: see text], where [Formula: see text] and list all permutation polynomials (PPs) and complete permutation polynomials (CPPs) of this form. This type of polynomials were studied by Bassalygo and Zinoviev for the cases [Formula: see text] and [Formula: see text], Wu, Li, Helleseth and Zhang for the case [Formula: see text], [Formula: see text], Bassalygo and Zinoviev answered the question for the case [Formula: see text], [Formula: see text] and finally by Bartoli et al. for the case [Formula: see text]. Here, we determine all PPs and CPPs for the case [Formula: see text].

Some classes of complete permutation polynomials over $\mathbb{F}_q $

2015 ◽  
Vol 58 (10) ◽  
pp. 1-14 ◽  
Author(s):  
GaoFei Wu ◽  
Nian Li ◽  
Tor Helleseth ◽  
YuQing Zhang
Keyword(s):  
Permutation Polynomials ◽  
Complete Permutation Polynomials

scholarly journals New classes of complete permutation polynomials

2019 ◽  
Vol 55 ◽  
pp. 177-201 ◽  
Author(s):  
Lisha Li ◽  
Chaoyun Li ◽  
Chunlei Li ◽  
Xiangyong Zeng
Keyword(s):  
Permutation Polynomials ◽  
Complete Permutation Polynomials

scholarly journals Further results on permutation polynomials and complete permutation polynomials over finite fields

2021 ◽  
Vol 6 (12) ◽  
pp. 13503-13514
Author(s):  
Qian Liu ◽  
◽  
Jianrui Xie ◽  
Ximeng Liu ◽  
Jian Zou ◽  
...  
Keyword(s):  
Finite Fields ◽  
Permutation Polynomials ◽  
Number Of Solutions ◽  
Polynomials Over Finite Fields ◽  
Agw Criterion ◽  
Complete Permutation Polynomials

<abstract><p>In this paper, by employing the AGW criterion and determining the number of solutions to some equations over finite fields, we further investigate nine classes of permutation polynomials over $ \mathbb{F}_{p^n} $ with the form $ (x^{p^m}-x+\delta)^{s_1}+(x^{p^m}-x+\delta)^{s_2}+x $ and propose five classes of complete permutation polynomials over $ \mathbb{F}_{p^{2m}} $ with the form $ ax^{p^m}+bx+h(x^{p^m}-x) $.</p></abstract>

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