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arXiv · 1806.05712

Permutation polynomials and complete permutation polynomials over $\mathbb{F}_{q^{3}}$

Yanping Wang·WeiGuo Zhang·Daniele Bartoli·Qiang Wang
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Abstract

Motivated by many recent constructions of permutation polynomials over $\mathbb{F}_{q^2}$, we study permutation polynomials over $\mathbb{F}_{q^3}$ in terms of their coefficients. Based on the multivariate method and resultant elimination, we construct several new classes of sparse permutation polynomials over $\mathbb{F}_{q^3}$, $q=p^{k}$, $p\geq3$. Some of them are complete mappings.

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Yanping Wang, WeiGuo Zhang, Daniele Bartoli, Qiang Wang. 2018-06-15. Permutation polynomials and complete permutation polynomials over $\mathbb{F}_{q^{3}}$. https://arxiv.org/abs/1806.05712

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