Further results on permutation polynomials and complete permutation polynomials over finite fields

In this paper, by employing the AGW criterion and determining the number of solutions to some equations over finite fields, we further investigate nine classes of permutation polynomials over F-pn with the form (x(pm) - x + delta)(s1) + (x(pm) - x + delta)(s2) + x and propose five classes of complete permutation polynomials over F-p2m with the form ax(pm) + bx + h(x(pm) - x).

Automated summary

This paper explores nine classes of permutation polynomials over F-pn and proposes five classes of complete permutation polynomials over F-p2m, based on AGW criterion and determination of solutions to equations over finite fields.