EN|RU Volume 15, No 3, 2008, P. 11-21 UDC 519.72 Yu. L. Vasil´ev, S. V. Avgustinovich, and D. S. Krotov On mobile sets in the binary hypercube Abstract: If two distance-3 codes have the same neighborhood, then each of them is called a mobile set. In the $(4k+3)$-dimensional binary hypercube there exists a mobile set of cardinality $2\cdot6^k$ that cannot be split into mobile sets of smaller cardinalities or represented as a natural extension of a mobile set of smaller dimension. Bibl. 10. Keywords: 1-perfect code, Bollean cube, mobile set, $i$-component. Vasil’ev Yuriy Leonidovich 1 Avgustinovich Sergey Vladimirovich 1 Krotov Denis Stanislavovich 1 1. S. L. Sobolev Institute of Mathematics, SB RAS, 4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia e-mail: vas@math.nsc.ru, avgust@math.nsc.ru, krotov@math.nsc.ru © Sobolev Institute of Mathematics, 2015