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arXiv · 1806.11473

On a conjecture on permutation polynomials over finite fields

Wun-Seng Chou·Xiang-dong Hou
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Abstract

Let $\Bbb F_q$ be the finite field with $q$ elements and let $p=\text{char}\,\Bbb F_q$. It was conjectured that for integers $e\ge 2$ and $1\le a\le pe-2$, the polynomial $X^{q-2}+X^{q^2-2}+\cdots+X^{q^a-2}$ is a permutation polynomial of $\Bbb F_{q^e}$ if and only if (i) $a=2$ and $q=2$, or (ii) $a=1$ and $\text{gcd}(q-2,q^e-1)=1$. In the present paper we confirm this conjecture.

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Wun-Seng Chou, Xiang-dong Hou. 2018-06-29. On a conjecture on permutation polynomials over finite fields. https://arxiv.org/abs/1806.11473

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