English

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.

Keywords

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)

R2 v1 2026-06-21T10:08:28.170Z