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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.

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Authors and Affiliations

  1. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    A. K. Oblaukhov

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  1. A. K. Oblaukhov
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Correspondence to A. K. Oblaukhov.

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Original Russian Text © A.K. Oblaukhov, 2016, published in Diskretnyi Analiz i Issledovanie Operatsii, 2016, Vol. 23, No. 3, pp. 93–106.

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Oblaukhov, A.K. Metric complements to subspaces in the Boolean cube. J. Appl. Ind. Math. 10, 397–403 (2016). https://doi.org/10.1134/S1990478916030108

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  • DOI: https://doi.org/10.1134/S1990478916030108

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