Geodesic
On the Limit Distribution of the Number of Solutions of a Random Linear System in the Glass of Boolean Functions
Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 1, pp. 51-61 
I. N. Kovalenko. On the Limit Distribution of the Number of Solutions of a Random Linear System in the Glass of Boolean Functions. Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 1, pp. 51-61. http://geodesic.mathdoc.fr/item/TVP_1967_12_1_a4/
@article{TVP_1967_12_1_a4,
     author = {I. N. Kovalenko},
     title = {On the {Limit} {Distribution} of the {Number} of {Solutions} of {a~Random} {Linear} {System} in the {Glass} of {Boolean} {Functions}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {51--61},
     year = {1967},
     volume = {12},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1967_12_1_a4/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let (1) be a system of linear Boolean equations, $a_{ij}$ being independent random variables with distributions given by (2). Let $\nu_n$ denote the number of linearly independent solutions of the system. Condition (3) with some fixed $\delta>0$ implies the convergence of the distributions of $\nu_n$ as $n\to\infty$ to the distribution of a random variable $\nu$ which can be constructed as follows: $$ \nu= \begin{cases} 0&\text{if}\quad m+s_{k_0}\le0 \\ m+s_{k_0}&\text{if}\quad m+s_{k_0}>0 \end{cases} $$ where die distribution of $s_{k_0}$ is given by (24), (25).