Two Absolutely Irreducible Polynomials over ${\mathbb{F}}_2$ and Their Applications to a Conjecture by Carlet

Xiang-dong Hou, Shujun Zhao

Two polynomials $F_k(X_1,\dots ,X_k)$ and ${\Theta }_k(X_1,\dots ,X_k)$ over ${\mathbb{F}}_2$ arose from the study of a conjecture by C. Carlet about the sum-freedom of the multiplicative inverse…