Geodesic
The number and cardinalities of components of solutions of a~discrete isoperimetric problem in the Hamming space
Diskretnaya Matematika, Tome 3 (1991) no. 4, pp. 28-46.

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We consider the problem of describing multicomponent subsets of the set $\{0, 1 \}^n$ having a minimal boundary in the Hamming metric. In the framework of this metric and of a natural understanding of components of a set, we establish 1) conditions for the existence of such subsets of a given cardinality with a given number of components; 2) attainable and other upper bounds for the number of components and their cardinalities depending on the cardinality of these subsets. In particular, we show that for $k\geq \sqrt{n-1}-1$ as $n\to \infty $ almost all points of such a subset of cardinality not less than $\sum^k_{i=0} (^n_i)$ are contained in a unique component. 
@article{DM_1991_3_4_a4,
     author = {B. E. Torosyan},
     title = {The number and cardinalities of components of solutions of a~discrete isoperimetric problem in the {Hamming} space},
     journal = {Diskretnaya Matematika},
     pages = {28--46},
     publisher = {mathdoc},
     volume = {3},
     number = {4},
     year = {1991},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1991_3_4_a4/}
}
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B. E. Torosyan. The number and cardinalities of components of solutions of a~discrete isoperimetric problem in the Hamming space. Diskretnaya Matematika, Tome 3 (1991) no. 4, pp. 28-46. http://geodesic.mathdoc.fr/item/DM_1991_3_4_a4/