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Metric complements to subspaces in the Boolean cube. (Russian, English) Zbl 1374.94798
Diskretn. Anal. Issled. Oper. 23, No. 3, 93-106 (2016); translation in J. Appl. Ind. Math. 10, No. 3, 397-403 (2016).
Summary: 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.

MSC:
94A60 Cryptography
94C10 Switching theory, application of Boolean algebra; Boolean functions (MSC2010)
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