Two Classes of Permutations in Trivariate Form over $\mathbb{F}_{2^m}^3$

Abstract

Permutations on the vector spaces $\mathbb{F}_{q}^n$ are few at present. Inspired by the work of Chi, Li and Qu [1], we construct two classes of permutations with 3-homogeneous structures in trivariate form over $\mathbb{F}_{2^m}^3$. To establish their permutation properties, we formulate a system of equations and analyze it using techniques such as resultants, multivariate methods, and the method of undetermined coefficients.