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Citation - Scopus: 3
Complete Characterization of a Class of Permutation Trinomials in Characteristic Five
(Springer, 2024) Grassl,M.; Özbudak,F.; Özkaya,B.; Temür,B.G.
In this paper, we address an open problem posed by Bai and Xia in [2]. We study polynomials of the form f(x)=x4q+1+λ1x5q+λ2xq+4 over the finite field F5k, which are not quasi-multiplicative equivalent to any of the known permutation polynomials in the literature. We find necessary and sufficient conditions on λ1,λ2∈F5k so that f(x) is a permutation monomial, binomial, or trinomial of F52k. © The Author(s) 2024.
Citation - WoS: 13
Citation - Scopus: 12
Classification of Permutation Polynomials of the Form x^{3< of F_{q2< Where g(x< = x^{3< + bx Plus c and b, c ∈ F_q<}}}
(Springer, 2022) Ozbudak, Ferruh; Temur, Burcu Gulmez
We classify all permutation polynomials of the form x(3) g(x(q-1)) of F-q2 where g(x) = x(3) + bx + c and b, c is an element of F-q*. Moreover we find new examples of permutation polynomials and we correct some contradictory statements in the recent literature. We assume that gcd(3, q -1) = 1 and we use a well known criterion due to Wan and Lidl, Park and Lee, Akbary and Wang, Wang, and Zieve.