Some new forms of permutation polynomials based on the AGW criterion.

• Seven permutation polynomials of the form x + (Tr m n (x) k + δ) s are presented. • Three permutation polynomials of the form x + (Tr m n (x) k 1 + δ) s 1 + (Tr m n (x) k 2 + δ) s 2 are presented. • Accordingly, corresponding proofs are given in detail. In this paper, we propose several classes of permutation polynomials over F 2 2 m of the form x + (Tr m n (x) k + δ) s and x + (Tr m n (x) k 1 + δ 1) s 1 + (Tr m n (x) k 2 + δ 2) s 2 based on the AGW criterion. [ABSTRACT FROM AUTHOR]