Consider linear $N$-dimensional space $F_2^N$. Consider its $K$ dimensional subspace $V \subset F_2^N$. Let us calculate $w(k,V,N)$ number of vectors in $V$ of Hamming weight $k$ in $V$.
Since there is finite number of subspaces we can calculate average: $\sum_{V} w(k,V,N)$.
Question is there something known about it ?
Coding theory motivation - is to understand how good/bad is a random linear code ? I.e. error-correcting code is precisely $V$ in $F_2^N$. Code is bad if we have many vectors of small Hamming weight.