Metric complements to subspaces in the Boolean cube

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Abstract

We study the metric complements to subsets in the Boolean cube, i.e. the subsets maximally distant from a given subset. We obtain the general form for the metric complement of a linear subspace and some more exact description for the class of subspaces with basis of a special form. It is proved that the completely regular codes (including perfect and uniformly packed) are metrically regular.

Keywords

subspace metrically regular set metric complement completely regular code bent-function 

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Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Novosibirsk State UniversityNovosibirskRussia

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