• Corpus ID: 15369757

On mobile sets in the binary hypercube

@article{Vasilev2008OnMS,
  title={On mobile sets in the binary hypercube},
  author={Yu. L. Vasil’ev and Sergey V. Avgustinovich and Denis S. Krotov},
  journal={ArXiv},
  year={2008},
  volume={abs/0802.0003}
}
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. 
2 Citations

The extended 1-perfect trades in small hypercubes

  • D. Krotov
  • Economics, Computer Science
    Discret. Math.
  • 2017

Embedding in a perfect code

A binary 1 ‐error‐correcting code can always be embedded in a 1 ‐perfect code of some larger length. © 2009 Wiley Periodicals, Inc. J Combin Designs 17: 419–423, 2009

References

SHOWING 1-10 OF 26 REFERENCES

Structure of i-components of perfect binary codes

A lower bound for the number of transitive perfect codes

In conclusion, pairwise nonequivalent transitive extended perfect codes of length 4n as n → ∞ are constructed.

On the Construction of Transitive Codes

Application of some known methods of code construction to transitive codes satisfying certain auxiliary conditions yields infinite classes of large-length transitivecodes, in particular, at least at least ⌊k/2⌋2 nonequivalent perfect transitives codes of length n = 2k − 1, k > 4.

On enumeration of nonequivalent perfect binary codes of length 15 and rank 15

All nonequivalent perfect binary codes of length 15 and rank 15 are constructed that are obtained from the Hamming code H15 by translating its disjoint components. Also, the main invariants of this

Binary extended perfect codes of length 16 and rank 14

It is proved that among allNonequivalent extended binary perfect (16, 4, 211) codes there are exactly 1719 nonequivalent codes of rank 14 over F2.

Perfect 2-colorings of a hypercube

A coloring of the vertices of a graph is called perfect if the multiset of colors of all neighbors of a vertex depends only on its own color. We study the possible parameters of perfect 2-colorings

Ñîâåðøåííûå 2ðàñêðàñêè ãèïåðêóáà / / Ñèáèðñêèéìàòåìàòè÷åñêèé æóðíàë

  • 2007

Codegenerating factorization on ndimensional unite cube and perfect binary codes

  • Probl. Inform. Transm. transl. from Probl. Peredachi Inf
  • 1997

Î ïîñòðîåíèè òðàíçèòèâíûõ êîäîâ / / Ïðîáëåìû ïåðåäà÷èèí  îðìàöèè

  • 2005

Solov’eva, On the construction of transitive codes, Probl

  • Inform. Transm
  • 2005