If such a set $ A$ of size $ m$ exists, all its admissible pairwise sums must lie in its complement, thus $ $ \binom{m}{2} \leq 2^n-m, $ $ which gives $ $ m\leq 2^{(n+1)/2}\qquad (1)$ $ . Since $ a+b=c$ is the same as $ a+b+c=0$ in characteristic 2, a randomly chosen set ofRead more