Geodesic
A multivariate Poisson theorem for the number of solutions of random inclusions close to given vectors
Matematičeskie voprosy kriptografii, Tome 7 (2016), pp. 67-80

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We consider the number of solutions of random inclusion over a finite field that differ from a reference vector by no more than a specified number of coordinates. We find conditions on the growth of vector dimensions under which the number of solutions close to some reference vectors are asymptotically independent and their distributions converge to the Poisson distributions. 
@article{MVK_2016_7_a4,
     author = {V. A. Kopytcev},
     title = {A multivariate {Poisson} theorem for the number of solutions of random inclusions close to given vectors},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {67--80},
     publisher = {mathdoc},
     volume = {7},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2016_7_a4/}
}
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V. A. Kopytcev. A multivariate Poisson theorem for the number of solutions of random inclusions close to given vectors. Matematičeskie voprosy kriptografii, Tome 7 (2016), pp. 67-80. http://geodesic.mathdoc.fr/item/MVK_2016_7_a4/