Classification of Rational Functions of Degree Three over Finite Fields

Xiang-dong Hou, Siyu Peng, Yongyu Qiang +1

We study rational functions over finite fields under PGL-equivalence. We say that $f,g\in {\mathbb{F}}_q(X)$ are \emph{equivalent} if there exist $\psi ,\varphi \in {\mathbb{F}}_q(X)$ of degree one su…