Explicit classes of permutation polynomials of $$ \mathbb{F}_{3^{3m} } $$.

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 $$ \mathbb{F}_{3^{3m} } $$ are presented. These polynomials have simple shapes, and they are related to planar functions. [ABSTRACT FROM AUTHOR]