Permutation binomials of the form $x^r(x^{q-1}+a)$ over ${\mathbb{F}}_{q^e}$

Ariane M. Masuda, Ivelisse Rubio, Javier Santiago

We present several existence and nonexistence results for permutation binomials of the form $x^r(x^{q-1}+a)$, where $e\ge 2$ and $a\in {\mathbb{F}}_{q^e}^{\ast }$. As a consequence, we ob…