Grassl, MarkusÖzbudak, FerruhÖzkaya, BuketGülmez Temür, Burcu2024-06-072024-06-072024-02-21https://hdl.handle.net/20.500.14411/20441936-2455https://doi.org/10.1007/s12095-024-00705-2Open Access; Published by Cryptography and Communications; https://doi.org/10.1007/s12095-024-00705-2; Markus Grassl, International Centre for Theory of Quantum Technologies, University of Gdansk, Gdansk, Poland; Ferruh Özbudak, FENS, Sabancı University, Ístanbul, Turkey; Buket Özkaya, Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey; Burcu Gülmez Temür, Department of Mathematics, Atılım University, Ankara, Turkey.In this paper, we address an open problem posed by Bai and Xia in [2].We study polynomials of the form f (x) = x^4q+1 + λ_1x^5q + λ_2x^q+4 over the finite field F_5^k , which are not quasimultiplicative equivalent to any of the known permutation polynomials in the literature. We find necessary and sufficient conditions on λ1, λ2 ∈ F_5^k so that f (x) is a permutation monomial, binomial, or trinomial of F_5^2k .enPermutation polynomialsFinite fieldsAbsolutely irreducibleMSC 11T0611T7112E10Article