EA-Equivalence
We call two \((m,n,p)\)-functions \(f(x)\) and \(g(x)\) extended affine equivalent (or EA-equivalent) provided there exist affine permutations \(A_1(x)\) and \(A_2(x)\), and an affine polynomial \(A(x)\) for which:
\[ g(x)=A_1 \circ f \circ A_2(x)+A(x) \] (sidenote: We have the following implication: EA-equivalence \(\implies\) affine equivalence )