Number of Equivalence Classes of Rational Functions over Finite Fields

Xiang-dong Hou

Two rational functions $f,g\in {\mathbb{F}}_q(X)$ are said to be {\em equivalent} if there exist $\ddot{I}•,\ddot{I}ˆ\in {\mathbb{F}}_q(X)$ of degree one such that $g=\ddot{I}•\circ f\circ \ddot{I}ˆ$. We give an explicit fo…