Metric complements to subspaces in the Boolean cube

We study the metric complements to sets in the Boolean cube; i.e. the subsets maximally distant from 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. Bibliogr. 9.