On Two Conjectures about Permutation Trinomials over $\mathbb{F}_{3^{2k}}$

Nian Li

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arXiv · 1610.04441

On Two Conjectures about Permutation Trinomials over $\mathbb{F}_{3^{2k}}$

Nian Li

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Abstract

Permutation polynomials with few terms attracts researchers' interest in recent years due to their simple algebraic form and some additional extraordinary properties. In this paper, by analyzing the quadratic factors of a fifth-degree polynomial and a seventh-degree polynomial over the finite field $\mathbb{F}_{3^{2k}}$, two conjectures on permutation trinomials over $\mathbb{F}_{3^{2k}}$ proposed recently by Li, Qu, Li and Fu are settled, where $k$ is a positive integer.

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Nian Li. 2016-10-14. On Two Conjectures about Permutation Trinomials over $\mathbb{F}_{3^{2k}}$. https://arxiv.org/abs/1610.04441

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