Some new results on permutation polynomials of the form b(xq+ax+δ

Danyao Wu,Pingzhi Yuan

This paper investigates the permutation behavior of polynomials in the form b(xpm+ax+δ)s−ax over Fp2m by employing the Akbary–Ghioca–Wang criterion, where b∈Fpm⁎, a,δ∈Fp2m with aq+1=1. As a result, we present several classes of permutation polynomials of the form b(x2m+ax+δ)s+ax over F22m and three classes of permutation polynomials of the form b(xpm−x+δ)s+x over Fp2m with infinitely many odd primes p.