Permutation trinomials over F2m

Permutation polynomials are an interesting subject of mathematics and have applications in other areas of mathematics and engineering. In this paper, we determine all permutation trinomials over F2m in Zieve's paper [30]. We prove a conjecture proposed by Gupta and Sharma in [8] and obtain some new permutation trinomials over F2m. Finally, we show that some classes of permutation trinomials with parameters are QM equivalent to some known permutation trinomials.