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Title: Permutations on finite fields with invariant cycle structure on lines
Author(s): Gerike, DanielLook up in the Integrated Authority File of the German National Library
Kyureghyan, Gohar M.Look up in the Integrated Authority File of the German National Library
Issue Date: 2020
Type: Article
Language: English
URN: urn:nbn:de:gbv:ma9:1-1981185920-645461
Subjects: Permutation polynomials
Cycle structure
Switching construction
Abstract: We study the cycle structure of permutations F(x) = x+γ f (x) onFqn,where f : Fqn → Fq . We show that for a 1-homogeneous function f the cycle structure of F can be determined by calculating the cycle structure of certain induced mappings on parallel lines of γ Fq. Using this observation we describe explicitly the cycle structure of two families of permutations over Fq2 : x + γ Tr(x2q−1), where q ≡ −1 (mod 3) and γ ∈ Fq2 , with γ 3 = − 1 27 and x + γ Tr x 22s−1+3·2s−1+1 3 , where q = 2s , s odd and γ ∈ Fq2 , with γ (q+1)/3 = 1.
Open Access: Open access publication
License: (CC BY 4.0) Creative Commons Attribution 4.0(CC BY 4.0) Creative Commons Attribution 4.0
Sponsor/Funder: Projekt DEAL 2020
Journal Title: Designs, codes and cryptography
Publisher: Springer Science + Business Media B.V
Publisher Place: Dordrecht [u.a.]
Volume: 88
Original Publication: 10.1007/s10623-020-00721-2
Page Start: 1723
Page End: 1740
Appears in Collections:Fakultät für Mathematik (OA)

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