On the rank of random binary matrix with fixed weights of independent rows

We consider random matrix consisting of $n$ independent rows such that each row is equiprobably chosen from the set of all $m$-dimensional ($m>n$) binary vectors with given weights $s_i$, $i=1,\ldots,n$, and study asymptotic properties of the rank of such matrix.
We propose explicit upper bound for the distribution function of the rank of matrixes.