Full Classification of permutation rational functions and complete rational functions of degree three over finite fields

Andrea Ferraguti, Giacomo Micheli

Let $q$ be a prime power, ${\mathbb{F}}_q$ be the finite field of order $q$ and ${\mathbb{F}}_q(x)$ be the field of rational functions over ${\mathbb{F}}_q$. In this paper we classify all r…