Four classes of permutation polynomials of

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 . 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.