All Questions

For $A\subseteq {\mathbb F}_2^n$ let $$ Q(A)=\{\alpha+\beta\mid \alpha,\beta \in A,\ \alpha\neq\beta \}. $$ I want to prove or disprove that if $|A|=2^k+1$ for some integer $k$, then $$ |Q(A)|\ge2^{k+...