Degree of Orthomorphism Polynomials over Finite Fields

Jack Allsop, Ian M. Wanless

An orthomorphism over a finite field ${\mathbb{F}}_q$ is a permutation $\theta :{\mathbb{F}}_q\mapsto {\mathbb{F}}_q$ such that the map $x\mapsto \theta (x)-x$ is also a permutation of ${\mathbb{F}}_q$.…