Permutation polynomials of the form cx + Tr q l / q ( x a ) $cx+\text {Tr}_{q^{l}/ q}(x^{a})$ and permutation trinomials over finite fields with even characteristic

2017 ◽  
Vol 10 (3) ◽  
pp. 531-554 ◽  
Author(s):  
Kangquan Li ◽  
Longjiang Qu ◽  
Xi Chen ◽  
Chao Li
Keyword(s):  
Finite Fields ◽  
Permutation Polynomials ◽  
Permutation Trinomials

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.

scholarly journals On the number of permutation polynomials over a finite field

2016 ◽  
Vol 12 (06) ◽  
pp. 1519-1528
Author(s):  
Kwang Yon Kim ◽  
Ryul Kim ◽  
Jin Song Kim
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Roots Of Unity ◽  
Permutation Polynomials

In order to extend the results of [Formula: see text] in [P. Das, The number of permutation polynomials of a given degree over a finite field, Finite Fields Appl. 8(4) (2002) 478–490], where [Formula: see text] is a prime, to arbitrary finite fields [Formula: see text], we find a formula for the number of permutation polynomials of degree [Formula: see text] over a finite field [Formula: see text], which has [Formula: see text] elements, in terms of the permanent of a matrix. We write down an expression for the number of permutation polynomials of degree [Formula: see text] over a finite field [Formula: see text], using the permanent of a matrix whose entries are [Formula: see text]th roots of unity and using this we obtain a nontrivial bound for the number. Finally, we provide a formula for the number of permutation polynomials of degree [Formula: see text] less than [Formula: see text].

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].

scholarly journals Some new results on permutation polynomials over finite fields

2016 ◽  
Vol 83 (2) ◽  
pp. 425-443 ◽  
Author(s):  
Jingxue Ma ◽  
Tao Zhang ◽  
Tao Feng ◽  
Gennian Ge
Keyword(s):  
Finite Fields ◽  
Permutation Polynomials ◽  
Polynomials Over Finite Fields
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