Permutation polynomials with low differential uniformity over finite fields of odd characteristic

2013 ◽  
Vol 56 (7) ◽  
pp. 1429-1440 ◽  
Author(s):  
WenJie Jia ◽  
XiangYong Zeng ◽  
ChunLei Li ◽  
Tor Helleseth ◽  
Lei Hu
Keyword(s):  
Finite Fields ◽  
Permutation Polynomials ◽  
Differential Uniformity

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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