Anbar Meidl, Nurdagül and Kaşıkçı, Canan (2021) Permutations polynomials of the form G(X)(k)  L(X) and curves over finite fields. Cryptography and Communications, 13 (2). pp. 283294. ISSN 19362447 (Print) 19362455 (Online)
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Official URL: http://dx.doi.org/10.1007/s12095020004659
Abstract
For a positive integer k and a linearized polynomial L(X), polynomials of the form P(X) = G(X)(k)  L(X) is an element of Fqn [X] are investigated. It is shown that when L has a nontrivial kernel and G is a permutation of Fqn, then P(X) cannot be a permutation if gcd( k, q(n)  1) > 1. Further, necessary conditions for P(X) to be a permutation of Fqn are given for the case that G(X) is an arbitrary linearized polynomial. The method uses plane curves, which are obtained via the multiplicative and the additive structure of Fqn, and their number of rational affine points.
Item Type:  Article 

Uncontrolled Keywords:  Curves/function fields; Permutation polynomials; Rational points/places 
Subjects:  Q Science > QA Mathematics > QA150272.5 Algebra 
Divisions:  Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics Faculty of Engineering and Natural Sciences 
Depositing User:  Nurdagül Anbar Meidl 
Date Deposited:  22 Mar 2021 19:08 
Last Modified:  22 Mar 2021 19:08 
URI:  https://research.sabanciuniv.edu/id/eprint/41366 
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Permutations polynomials of the form G(X)(k)  L(X) and curves over finite fields. (deposited 20 Feb 2021 17:36)
 Permutations polynomials of the form G(X)(k)  L(X) and curves over finite fields. (deposited 22 Mar 2021 19:08) [Currently Displayed]