Advertisement

Designs, Codes and Cryptography

, Volume 3, Issue 2, pp 95–98 | Cite as

A sharpening of the Johnson bound for binary linear codes and the nonexistence of linear codes with preparata parameters

  • A. E. Brouwer
  • L. M. G. M. Tolhuizen
Article

Abstract

We show fort>3 the nonexistence of binary [2 t −2, 2 t −2t−1, 5] codes.

Keywords

Data Structure Information Theory Discrete Geometry Linear Code Binary Linear Code 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Brouwer, A.E. 1992.The linear programming bound for binary linear codes. PreprintIEEE Trans. Inf. Th., submitted.Google Scholar
  2. 2.
    Brouwer, A.E. and Verhoeff, T.An updated table of minimum-distance bounds for binary linear codes, preprint (March 1992). (IEEE Trans. Inf. Th., to appear)Google Scholar
  3. 3.
    Dodunekov, S.M. and Zinoviev, V.A. 1984.A note on Preparata codes. InProc. of the 6th Intern. Symp. Inform. Th., Tashkent 1984, 1984.Google Scholar
  4. 4.
    Goethals, J.-M. and Snover, S.L., 1972.Nearly perfect binary codes.Discrete Math. 3:65–88.Google Scholar
  5. 5.
    Johnson, S.M. 1962.A new upper bound for error correcting codes, IRE Trans. Inform. Th. IT-8:203–207.Google Scholar
  6. 6.
    MacWilliams, F.J. and Sloane, N.J.A. 1977.The Theory of Error-Correcting Codes, North Holland Publ. Co., Amsterdam.Google Scholar
  7. 7.
    Preparata, F.P. 1968.A class of optimum nonlinear double-error correcting codes.Inf. & Control 13: 378–400.Google Scholar
  8. 8.
    Wax, N. 1959.On upper bounds for error detecting and error correcting codes of finite length.IEEE Trans. Info. Theory 5:168–174.Google Scholar

Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • A. E. Brouwer
    • 1
  • L. M. G. M. Tolhuizen
    • 2
  1. 1.Department of Math.Eindhoven Univ. of TechnologyEindhovenThe Netherlands
  2. 2.Philips Research LaboratoriesEindhovenThe Netherlands

Personalised recommendations