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arXiv · 1304.2254

Proof of a Conjecture on Permutation Polynomials over Finite Fields

Xiang-dong Hou
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Abstract

Let $k$ be a positive integer and $S_{2k}={\tt x}+{\tt x}^4+...+{\tt x}^{4^{2k-1}}\in\Bbb F_2[{\tt x}]$. It was recently conjectured that ${\tt x}+S_{2k}^{4^{2k}}+S_{2k}^{4^k+3}$ is a permutation polynomial of $\Bbb F_{4^{3k}}$. In this note, the conjecture is confirmed and a generalization is obtained.

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Xiang-dong Hou. 2013-04-08. Proof of a Conjecture on Permutation Polynomials over Finite Fields. https://arxiv.org/abs/1304.2254

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