ON SOME CLASSES OF PERMUTATION POLYNOMIALS
Amir Akbary, SEAN ALARIC, Qiang Wang · International Journal of Number Theory · 2008
Let p be a prime and q = pm. We investigate permutation properties of polynomials P(x) = xr + xr+s + ⋯ + xr+ks (0 < r < q - 1, 0 < s < q - 1, and k ≥ 0) over a finite field 𝔽q. More specifically, we construct several classes of permutation polynomials of this form over 𝔽q. We also count the number of permutation polynomials in each class.