Mao-Sheng Xiong

Characterization of a class of complete permutation quadrinomials over $\mathbb{F}_{2^{2m}}$

Let $q=2^m$, $Q=2^k$, and $1\leq k\leq m-1$. We characterize complete permutation polynomials (CPPs) over $\mathbb{F}_{q^2}$ of the form \[ f(x)=c_0x^{Q+1}+c_1x^{Q+q}+c_2x^{qQ+1} +c_3x^{q(Q+1)},\qquad c_i\in\mathbb{F}_{q^2}. \] We prove that no such CPP exists when $k>1$, and recover the known characterization in the c...