All Questions

Given an $m$ by $n$ matrix $M$ with $m \leq n$ and elements from $\{-1,1\}$, let us define: $$S_M = |\{Mx : x \in \{-1,1\}^n\}.$$ It is NP-hard to compute $S_M$ exactly I believe by applying the ...

Let $q$ be a fixed prime, $P, Q$ be polynomials with $\mathrm{deg}(Q) < \mathrm{deg}(P)$ and $h = O(\log n)$. Let $S$ be a subset of $\mathbb{F}_q^n$ of size $P(n)$ such that there exists a subset ...