On maximal metrically regular sets | Applied Discrete Mathematics. Supplement. 2017. № 10. DOI: 10.17223/2226308X/10/8

HomeIssuesOn maximal metrically regular sets | Applied Discrete Mathematics. Supplement. 2017. № 10. DOI: 10.17223/2226308X/10/8

On maximal metrically regular sets

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.

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Keywords

метрически регулярное множество, метрическое дополнение, минимальный покрывающий код, metrically regular set, metric complement, minimal covering code

Authors

NameOrganizationE-mail
Oblaukhov A. K.Novosibirsk State Universityoblaukhov@gmail.com
Всего: 1

References

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On maximal metrically regular sets | Applied Discrete Mathematics. Supplement. 2017. № 10. DOI: 10.17223/2226308X/10/8

On maximal metrically regular sets | Applied Discrete Mathematics. Supplement. 2017. № 10. DOI: 10.17223/2226308X/10/8