Theoretical Foundations of Applied Discrete Mathematics

On maximal metrically regular sets

A. K. Oblaukhov

Novosibirsk State University, Novosibirsk

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.

UDC: 519.7

DOI: 10.17223/2226308X/10/8