2 results
Search Results
Now showing 1 - 2 of 2
Article Citation - Scopus: 3Complete 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.Article On a Class of Permutation Trinomials Over Finite Fields(Tubitak Scientific & Technological Research Council Turkey, 2024) Temür, Burcu Gülmez; Özkaya, BuketIn this paper, we study the permutation properties of the class of trinomials of the form f (x) = x4q+1 + λ1xq+4 + λ2x2q+3 ∈ Fq2 [x] , where λ1, λ2 ∈ Fq and they are not simultaneously zero. We find all necessary and sufficient conditions on λ1 and λ2 such that f (x) permutes Fq2 , where q is odd and q = 22k+1, k ∈