Four classes of permutation polynomials of Fm2

Permutation polynomials have been a subject of study for over 140 years and have applications in many areas of science and engineering. However, only a handful of specific classes of permutation polynomials are known so far. In this paper we describe four classes of permutation polynomials over Fm2. Two of the four classes have the same form, while the other two classes are of different forms. Our work is motivated by a recent paper by Helleseth and Zinoviev.