Skip to main content

The domain of covering codes

  • 804 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 1518)

Abstract

In this paper the relationship between the normalised covering radius and the rate is considered for both linear and unrestricted codes. We characterise explicitly, for both cases, the region in the unit square where this type of behaviour is possible and show that certain types of asymptotic properties are wholly dependent upon it.

Keywords

  • Limit Point
  • Linear Code
  • Covering Radius
  • Covering Code
  • Modular Curf

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.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   69.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G. Cohen and P. Frankl; Good coverings of Hamming spaces with spheres; Discrete Math. 56 (1985), 125–131.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. G.D. Cohen, M.R. Karpovsky, H.F. Mattson, Jr., and J.R. Schatz, Covering radius: Survey and recent results; IEEE Trans. Inform. Theory 31 (1985), 328–343.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. J.H. van Lint; Introduction to coding theory, New York: Springer-Verlag, 1982.

    CrossRef  MATH  Google Scholar 

  4. F.J. MacWilliams and N.J.A. Sloane: The theory of error-correcting codes, Amsterdam: North-Holland, 1977.

    MATH  Google Scholar 

  5. Yu.I. Manin, What is the maximum number of points on a curve over F 2?, J. Fac. Sci. Univ. Tokyo 28 (1981), 715–720.

    MathSciNet  MATH  Google Scholar 

  6. G.F. Simmons; Introduction to topology and modern analysis, New York: McGraw-Hill, 1963.

    MATH  Google Scholar 

  7. S.G. Vladut and Yu.I. Manin; Linear codes and modular curves, Itogi Nauki i Tekhniki, Seriya Sovremennye Problemy Matematiki, Noveishie Dostizheniya 25 (1984), 209–257.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1992 Springer-Verlag

About this paper

Cite this paper

Stokes, P. (1992). The domain of covering codes. In: Stichtenoth, H., Tsfasman, M.A. (eds) Coding Theory and Algebraic Geometry. Lecture Notes in Mathematics, vol 1518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088000

Download citation

  • DOI: https://doi.org/10.1007/BFb0088000

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55651-0

  • Online ISBN: 978-3-540-47267-4

  • eBook Packages: Springer Book Archive