2 problems

Let $f: \{0,\ldots,q-1\}^n \rightarrow \{0,1\}$ be a function with $B$ zeros and $C$ ones, where $q\geq 3$. Suppose that for some $k$, every $k$-face has the same number … of ones…

Generalized correlation-immunity bound. If there exists a $(b,c)$-coloring in $H(n,q)$ with $b'+c'>q$, then