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