SOME FAMILIES OF PERMUTATION POLYNOMIALS OVER FINITE FIELDS
Michael E. Zieve · International Journal of Number Theory · 2008
We give necessary and sufficient conditions for a polynomial of the form xr(1 + xv + x2v + ⋯ + xkv)t to permute the elements of the finite field 𝔽q. Our results yield especially simple criteria in case (q - 1)/ gcd (q - 1, v) is a small prime.