Linear Functions A function \(f\colon F_2^n \to F_2\) is linear if \(f(x+y) = f(x) +f(y)\) for all \(x,y\in F_2^n\). Equivalently, \(f\) is linear if and only if there exists \(a\in F_2^n\) such that \(f(x) = ax\), or there exists \(S\subseteq…

Linear Functions A function \(f\colon F_2^n \to F_2\) is linear if \(f(x+y) = f(x) +f(y)\) for all \(x,y\in F_2^n\). Equivalently, \(f\) is linear if and only if there exists \(a\in F_2^n\) such that \(f(x) = ax\), or there exists \(S\subseteq…