Determination of all complete mappings of F_{q^2} of the form aX^{3q}+bX^{2q+1}+cX^{q+2}+dX^3

Zhiguo Ding, Wei Xiong, Michael E. Zieve

For each prime power q, we determine all polynomials over F_{q^2} of the form f(X) := aX^{3q}+bX^{2q+1}+cX^{q+2}+dX^3 which induce complete mappings of F_{q^2}, in the sense that e…