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arXiv · 1712.10017

On a conjecture about a class of permutation trinomials

Daniele Bartoli
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Abstract

We prove a conjecture by Tu, Zeng, Li, and Helleseth concerning trinomials $f_{α,β}(x)= x + αx^{q(q-1)+1} + βx^{2(q-1)+1} \in \mathbb{F}_{q^2}[x]$, $αβ\neq 0$, $q$ even, characterizing all the pairs $(α,β)\in \mathbb{F}_{q^2}^2$ for which $f_{α,β}(x)$ is a permutation of $\mathbb{F}_{q^2}$.

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Daniele Bartoli. 2017-12-28. On a conjecture about a class of permutation trinomials. https://arxiv.org/abs/1712.10017

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