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arXiv · 2406.15322

Permutation polynomials of finite fields of even characteristic from character sums

Ruikai Chen·Sihem Mesnager
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Abstract

In this paper, we investigate permutation polynomials over the finite field $\mathbb F_{q^n}$ with $q=2^m$, focusing on those in the form $\mathrm{Tr}(Ax^{q+1})+L(x)$, where $A\in\mathbb F_{q^n}^*$ and $L$ is a $2$-linear polynomial over $\mathbb F_{q^n}$. By calculating certain character sums, we characterize these permutation polynomials and provide additional constructions.

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Ruikai Chen, Sihem Mesnager. 2024-06-21. Permutation polynomials of finite fields of even characteristic from character sums. https://doi.org/10.1016/j.ffa.2025.102684

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