Geodesic
On the number of solutions of systems of linear Boolean equations in a set of vectors with a given number of ones
Diskretnaya Matematika, Tome 14 (2002) no. 4, pp. 87-109.

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We consider the distribution of the number of solutions of systems of random Boolean equations in the set of vectors with a given number of ones (or of a given weight). Both for systems with independent left-hand and right-hand sides and for a fortiori consistent systems, we give sufficient conditions for the distributions to converge to the Poisson law and to the standard normal law. 
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V. A. Kopyttsev. On the number of solutions of systems of linear Boolean equations in a set of vectors with a given number of ones. Diskretnaya Matematika, Tome 14 (2002) no. 4, pp. 87-109. http://geodesic.mathdoc.fr/item/DM_2002_14_4_a2/

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