On mobile sets in the binary hypercube
  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*6^k that cannot be split into mobile sets of smaller cardinalities or represented as a natural extension of a mobile set in a hypercube of smaller dimension. Keywords: mobile set; 1-perfect code. 
Yuriy Vasil'ev (Sobolev Institute of Mathematics, Novosibirsk,   Russia), Sergey Avgustinovich (Sobolev Institute of Mathema...