Testing Linear-Invariant Function Isomorphism

Karl Wimmer, Yuichi Yoshida

Abstract: A function \(f:\mathbb{F}_2^n \to \{-1,1\}\) is called linear-isomorphic to g if f = g ∘ A for some non-singular matrix A. In the g-isomorphism problem, we want a randomized algorithm that distinguishes whether an input function f is linear-isomorphic to g or far from being so.