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arXiv · 1312.5283

Determination of a Type of Permutation Binomials over Finite Fields

Xiang-dong Hou·Stephen D. Lappano
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Abstract

Let $f=a\x+\x^{3q-2}\in\Bbb F_{q^2}[\x]$, where $a\in\Bbb F_{q^2}^*$. We prove that $f$ is a permutation polynomial of $\Bbb F_{q^2}$ if and only if one of the following occurs: (i) $q=2^e$, $e$ odd, and $a^{\frac{q+1}3}$ is a primitive $3$rd root of unity. (ii) $(q,a)$ belongs to a finite set which is determined in the paper.

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Xiang-dong Hou, Stephen D. Lappano. 2013-12-21. Determination of a Type of Permutation Binomials over Finite Fields. https://arxiv.org/abs/1312.5283

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