Gülmez Temür, BurcuOzbudak, FerruhTemur, Burcu GulmezMathematics2024-07-052024-07-05202331071-57971090-246510.1016/j.ffa.2022.1021582-s2.0-85146438703https://doi.org/10.1016/j.ffa.2022.102158https://hdl.handle.net/20.500.14411/2597Ozbudak, Ferruh/0000-0002-1694-9283In this paper, we completely determine all necessary and sufficient conditions such that the polynomial f(x) = x3 + axq +2 + bx2q +1 + cx3q, where a, b, c is an element of Fq*, is a permutation quadrinomial of Fq2 over any finite field of odd characteristic. This quadrinomial has been studied first in [25] by Tu, Zeng and Helleseth, later in [24] Tu, Liu and Zeng revisited these quadrinomials and they proposed a more comprehensive characterization of the coefficients that results with new permutation quadrinomials, where char(Fq) = 2 and finally, in [16], Li, Qu, Li and Chen proved that the sufficient condition given in [24] is also necessary and thus completed the solution in even characteristic case. In [6] Gupta studied the permutation properties of the polynomial x3 + axq +2 + bx2q +1 + cx3q, where char(Fq) = 3, 5 and a, b, c is an element of Fq* and proposed some new classes of permutation quadrinomials of Fq2 . In particular, in this paper we classify all permutation polynomials of Fq2 of the form f(x) = x3 + axq +2 + bx2q +1 + cx3q, where a, b, c is an element of Fq*, over all finite fields of odd characteristic and obtain several new classes of such permutation quadrinomials. (c) 2022 Elsevier Inc. All rights reserved.eninfo:eu-repo/semantics/closedAccessPermutation polynomialsFinite fieldsAbsolutely irreducibleArticleQ2Q387WOS:000959588800001