Geodesic
Metric complements to subspaces in the Boolean cube
Diskretnyj analiz i issledovanie operacij, Tome 23 (2016) no. 3, pp. 93-106.

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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.
Keywords: subspace, metrically regular set, metric complement, completely regular code, bent-function. 
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A. K. Oblaukhov. Metric complements to subspaces in the Boolean cube. Diskretnyj analiz i issledovanie operacij, Tome 23 (2016) no. 3, pp. 93-106. http://geodesic.mathdoc.fr/item/DA_2016_23_3_a5/

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