Geodesic
On the rank of random binary matrix with fixed weights of independent rows
Matematičeskie voprosy kriptografii, Tome 10 (2019), pp. 67-76

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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. 
@article{MVK_2019_10_a4,
     author = {V. I. Kruglov and V. G. Mikhailov},
     title = {On the rank of random binary matrix with fixed weights of independent rows},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {67--76},
     publisher = {mathdoc},
     volume = {10},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2019_10_a4/}
}
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V. I. Kruglov; V. G. Mikhailov. On the rank of random binary matrix with fixed weights of independent rows. Matematičeskie voprosy kriptografii, Tome 10 (2019), pp. 67-76. http://geodesic.mathdoc.fr/item/MVK_2019_10_a4/