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Prikladnaya Diskretnaya Matematika. Supplement, 2017, Issue 10, Pages 23–24
DOI: https://doi.org/10.17223/2226308X/10/8 (Mi pdma350) 		 
Theoretical Foundations of Applied Discrete Mathematics

On maximal metrically regular sets

A. K. Oblaukhov

Novosibirsk State University, Novosibirsk
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DOI: https://doi.org/10.17223/2226308X/10/8
Abstract: 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.
Funding agency Grant number
Russian Foundation for Basic Research 17-41-543364
Document Type: Article
UDC: 519.7
Language: Russian
Citation: A. K. Oblaukhov, “On maximal metrically regular sets”, Prikl. Diskr. Mat. Suppl., 2017, no. 10, 23–24
Citation in format AMSBIB
\Bibitem{Obl17}
\by A.~K.~Oblaukhov
\paper On maximal metrically regular sets
\jour Prikl. Diskr. Mat. Suppl.
\yr 2017
\issue 10
\pages 23--24
\mathnet{http://mi.mathnet.ru/pdma350}
\crossref{https://doi.org/10.17223/2226308X/10/8}
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