Determination of a Type of Permutation Trinomials over Finite Fields

Xiang-dong Hou

Let $f=a\mathtt{x}+b{\mathtt{x}}^q+{\mathtt{x}}^{2q-1}\in {\mathbb{F}}_q[\mathtt{x}]$. We find explicit conditions on $a$ and $b$ that are necessary and sufficient for $f$ to be a permutation polynomial…