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# How many vectors of Hamming weight L in "random" K dimensional subspace of F_2^N ? Or how good/bad is random linear block code ?

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.

http://en.wikipedia.org/wiki/Hamming_weight