Geodesic
On maximal metrically regular sets
Prikladnaya Diskretnaya Matematika. Supplement, no. 10 (2017), pp. 23-24

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Metrically regular subsets of the Boolean cube are studied. It is proved that the metrically regular sets of maximal cardinality have covering radius 1 and are the complements of minimal covering codes of radius 1. A lower bound of the sum of cardinalities of two metrically regular sets, each being the metric complement of the other, is obtained. We conjecture that any minimal covering code is a metrically regular set.
Keywords: metrically regular set, metric complement, minimal covering code. 
@article{PDMA_2017_10_a7,
     author = {A. K. Oblaukhov},
     title = {On maximal metrically regular sets},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {23--24},
     publisher = {mathdoc},
     number = {10},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2017_10_a7/}
}
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A. K. Oblaukhov. On maximal metrically regular sets. Prikladnaya Diskretnaya Matematika. Supplement, no. 10 (2017), pp. 23-24. http://geodesic.mathdoc.fr/item/PDMA_2017_10_a7/