Permutation polynomials of the form x + L(x) over Fq3

2021 ◽  
Vol 76 ◽  
pp. 101906
Author(s):  
Tingting Pang ◽  
Yunge Xu ◽  
Nian Li ◽  
Xiangyong Zeng
Keyword(s):  
Permutation Polynomials

scholarly journals Two types of permutation polynomials with special forms

2019 ◽  
Vol 56 ◽  
pp. 1-16 ◽  
Author(s):  
Dabin Zheng ◽  
Mu Yuan ◽  
Long Yu
Keyword(s):  
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.

scholarly journals Permutation polynomials over Galois fields of characteristic

2021 ◽  
Vol 13 (2) ◽  
pp. 84-86
Author(s):  
Z.L. Dahiru ◽  
A.M. Lawan
Keyword(s):  
Permutation Polynomial ◽  
Permutation Polynomials ◽  
Galois Fields ◽  
Characteristic 2

In this paper, a class of permutation polynomial known as o-polynomial over Galois fields of characteristic 2 was studied. A necessary and sufficients condition for a monomial 𝑥2k to be an o-polynomial over F2t  is given and two results obtained by Gupta and Sharma (2016) were deduced.

scholarly journals A Class of New Permutation Polynomials over F 2 n

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Qian Liu ◽  
Ximeng Liu ◽  
Jian Zou
Keyword(s):  
Necessary Conditions ◽  
Permutation Polynomials ◽  
Sufficient And Necessary Conditions

In this paper, according to the known results of some normalized permutation polynomials with degree 5 over F 2 n , we determine sufficient and necessary conditions on the coefficients b 1 , b 2 ∈ F 2 n 2 such that f x = x 3 x ¯ 2 + b 1 x 2 x ¯ + b 2 x permutes F 2 n . Meanwhile, we obtain a class of complete permutation binomials over F 2 n .

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].

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