Akademik Veri Yönetim Sistemi
HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.54, sa.3, ss.797-806, 2025 (SCI-Expanded, Scopus, TRDizin)
In this paper, we determine the permutation properties of the polynomial x3 +xq +2-x4q-1 over the finite field Fq2 in characteristic three. Moreover, we consider the trinomials of the form x4q-1 + x2q +1 +/- x3.In particular, we first show that x3 + xq +2-x4q-1 permutes Fq2 with q = 3m if and only if m is odd. This enables us to show that the sufficient condition in [34, Theorem 4] is also necessary. Next, we prove that x4q-1 + x2q +1-x3 permutes Fq2 with q = 3m if and only if m not equivalent to 0 (mod 4). Consequently, we prove that the sufficient condition in [20, Theorem 3.2] is also necessary. Finally, we investigate the trinomial x4q-1 + x2q +1 + x3 and show that it is never a permutation polynomial of Fq2 in any characteristic. All the polynomials considered in this work are not quasi-multiplicative equivalent to any known class of permutation trinomials.