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tag it.inf-theory added
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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.
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