Skip to main content
SpringerLink
Log in

On a conjecture concerning coverings of Hamming space

  • Conference paper
  • First Online:
Applied Algebra, Algorithmics and Error-Correcting Codes (AAECC 1984)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 228))

Abstract

We provide evidence for the following conjecture: a minimal covering of the binary Hamming space F n+22 by spheres of radius t+1 has at most the same cardinality as a minimal covering of F n2 by spheres of radius t.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G. D. Cohen, M. R. Karpovsky, H. F. Mattson, Jr. and J. R. Schatz, Covering Radius — Survey and Recent Results, IEEE Trans. Inform. Theory, IT-31 (1985), 328–343.

    Google Scholar 

  2. A. C. Lobstein, G. D. Cohen and N. J. A. Sloane, Recouvrements d'espaces de Hamming binaires, Comptes Rendus Acad. Sci. Paris, Série I, 301 (1985), 135–138.

    Google Scholar 

  3. R. L. Graham and N. J. A. Sloane, On the Covering Radius of Codes, IEEE Trans. Inform. Theory, IT-31 (1985), 385–401.

    Google Scholar 

  4. A. C. Lobstein, Contributions au codage combinatoire: ordres additifs, rayon de recouvrement, These de docteur-ingenieur, Paris, 1985.

    Google Scholar 

  5. T. Helleseth, T. Klove and J. Mykkeltveit, On the Covering Radius of Binary Codes, IEEE Trans. Inform. Theory, IT-24 (1978), 627–628.

    Google Scholar 

  6. G. D. Cohen, A. C. Lobstein and N. J. A. Sloane, Further results on the covering radius of codes, IEEE Trans. Inform. Theory, (1986), to appear.

    Google Scholar 

  7. N. J. A. Sloane, A new approach to the covering radius of codes, J. Combinatorial Theory (1986), to appear.

    Google Scholar 

  8. K. E. Kilby and N. J. A. Sloane, On the covering radius problem for codes: (I) Bounds on normalized covering radius, SIAM J. Alg. Disc. Methods, to appear.

    Google Scholar 

  9. K. E. Kilby and N. J. A. Sloane, On the covering radius problem for codes: (II) Codes of low dimension; normal and abnormal codes, SIAM J. Alg. Disc. Methods, to appear.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Ecole Nationale Supérieure des Téécommunications, 46 rue Barrault, 75634, Paris Cedex 13, France

    G. D. Cohen & A. C. Lobstein

  2. AT&T Bell Laboratories, 07974, Murray Hill, NJ, USA

    N. J. A. Sloane

Authors
  1. G. D. Cohen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. C. Lobstein
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. N. J. A. Sloane
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Alain Poli

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Cohen, G.D., Lobstein, A.C., Sloane, N.J.A. (1986). On a conjecture concerning coverings of Hamming space. In: Poli, A. (eds) Applied Algebra, Algorithmics and Error-Correcting Codes. AAECC 1984. Lecture Notes in Computer Science, vol 228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16767-6_52

Download citation

  • DOI: https://doi.org/10.1007/3-540-16767-6_52

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16767-9

  • Online ISBN: 978-3-540-38813-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation