On mobile sets in the binary hypercube
Combinatorics
2008-08-06 v1 Information Theory
math.IT
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*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.
Cite
@article{arxiv.0802.0003,
title = {On mobile sets in the binary hypercube},
author = {Yuriy Vasil'ev and Sergey Avgustinovich and Denis Krotov},
journal= {arXiv preprint arXiv:0802.0003},
year = {2008}
}
Comments
9p., in Russian (English version will be finished later)