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Permutation polynomials and complete permutation polynomials over $\mathbb{F}_{q^{3}}$
Yanping Wang, WeiGuo Zhang, Daniele Bartoli, Qiang Wang · 2018-06-15 · via cs.IT updates on arXiv.org

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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