On shifting sets in the binary hypercube
Yu. L. Vasil’ev, S. V. Avgustinovich, Denis S. Krotov · Journal of Applied and Industrial Mathematics · 2009
If two codes with distance 3 have some coincident neighborhoods then each of them is called a shifting set. In the binary (4k + 3)-dimensional hypercube, there exists a shifting set of power 2 · 6 k which can be neither divided into shifting sets of less size nor represented as a natural dilatation of a shifting set of less size.