Geodesic
Perfect multiple coverings of hypercube
Diskretnyj analiz i issledovanie operacij, Tome 19 (2012) no. 4, pp. 60-65

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A subset $C$ of graph vertices is called a perfect $k$-multiple covering with a radius $r$ if every vertex of this graph is within distance $r$ from exactly $k$ vertices of $C$. We give a criterion based on parameters of a perfect coloring. This criterion determines whether the perfect coloring is a perfect multiple covering with fixed radius $r\geq1$ of some multiplicity. Bibliogr. 13.
Mots-clés : hypercube
Keywords: perfect coloring, perfect code, perfect multiple coverings. 
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     title = {Perfect multiple coverings of hypercube},
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K. V. Vorob'ev. Perfect multiple coverings of hypercube. Diskretnyj analiz i issledovanie operacij, Tome 19 (2012) no. 4, pp. 60-65. http://geodesic.mathdoc.fr/item/DA_2012_19_4_a4/