Some classes of permutation polynomials of the form b(xq + ax + δ)i(q2-1)/d+1 + c(xq + ax + δ)j(q2-1)/d+1 + L(x) over Fq2

Let s be a prime power and F-q be a finite field with s elements. In this paper, we employ the AGW criterion to investigate the permutation behavior of some polynomials of the form b(x(q) + ax + delta)(i(q2-1)/d+1) + c(x(q) + ax + delta)(j(q2-1)/d+1) + L(x) over F-q2 with a(1+q) = 1, q = +/- 1 (mod d) and L(x) = -ax or x(q) - ax. Accordingly, we also present the permutation polynomials of the form b(x(q) + ax + delta)(s) - ax by letting c = 0 and choosing some special exponent s, which generalize some known results on permutation polynomials of this form.

Automated summary

In this paper, the permutation behavior of a class of polynomials over finite fields is investigated using the AGW criterion. The results are generalized by introducing special exponents s.