Given a function $F:\mathbb{Z}_{2}^{n} \to \mathbb{Z}_{2}^{n}$ (We can asume that is in algebraic normal form)
I need to find the max value of $C(A)$ over all $A$ invertible matrices with binary entries, $A$ different than the identity, of $\mathbb{Z}_{2}^{n}$ where $C(A)$ is the size of the set $\{ x: x\in \mathbb{Z}_{2}^{n} \text{ s.t } A(F(x)) = F(x)\}$
I have tried to find the fixed points of the invertible matrix with n=2 and n=3 (which is a lower bound for my solution), and apparently the only fix point is the zero vector.