Explicit classes of permutation polynomials of F-33m

Permutation polynomials have been an interesting subject of study for a long time and have applications in many areas of mathematics and engineering. However, only a small number of specific classes of permutation polynomials are known so far. In this paper, six classes of linearized permutation polynomials and six classes of nonlinearized permutation polynomials over F3 3m are presented. These polynomials have simple shapes, and they are related to planar functions.