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Permutations polynomials of the form G(X)(k) - L(X) and curves over finite fields

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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. 283-294. ISSN 1936-2447 (Print) 1936-2455 (Online)

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Official URL: http://dx.doi.org/10.1007/s12095-020-00465-9

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 F-qn [X] are investigated. It is shown that when L has a non-trivial kernel and G is a permutation of F-qn, 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 F-qn 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 F-qn, 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 > QA150-272.5 Algebra
ID Code:41366
Deposited By:Nurdagül Anbar Meidl
Deposited On:22 Mar 2021 19:08
Last Modified:22 Mar 2021 19:08

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