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

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 ${\mathbb{F}}_{q^3}$, $q=p^k$, $p\ge 3$. Some of them are complete mappings.

31 pages