Determination of a Type of Permutation Binomials over Finite Fields

Xiang-dong Hou, Stephen D. Lappano

Let $f=a\x+\x^{3q-2}\in\Bbb F_{q^2}[\x]$, where $a\in {\mathbb{F}}_{q^2}^{\ast }$. We prove that $f$ is a permutation polynomial of ${\mathbb{F}}_{q^2}$ if and only if one of the following occurs: (i…