A Note on a Class of Permutation Polynomials

Permutation polynomials have important applications in cryptography, coding theory, combinatorial designs, and other areas of mathematics and engineering. Finding new classes of permutation polynomials is therefore an interesting subject of study. In this paper, two new classes of permutation polynomials over finite fields are presented. Based on the link between equivalent equations and permutation polynomials, some other new permutation polynomials are also obtained. This note is a further study on the recent work of Zha and Hu, Li, Helleseth and Tang.