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arXiv · 2009.10851

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

Ariane M. Masuda·Ivelisse Rubio·Javier Santiago
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Abstract

We present several existence and nonexistence results for permutation binomials of the form $x^r(x^{q-1}+a)$, where $e\geq 2$ and $a\in \mathbb{F}_{q^e}^*$. As a consequence, we obtain a complete characterization of such permutation binomials over $\mathbb{F}_{q^2}$, $\mathbb{F}_{q^3}$, $\mathbb{F}_{q^4}$, $\mathbb{F}_{p^5}$, and $\mathbb{F}_{p^6}$, where $p$ is an odd prime.

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Ariane M. Masuda, Ivelisse Rubio, Javier Santiago. 2020-09-22. Permutation binomials of the form $x^r(x^{q-1}+a)$ over $\mathbb F_{q^e}$. https://arxiv.org/abs/2009.10851

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