Skip to main content

The Minimum Hamming Distance of Cyclic Codes of Length 2p s

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5527))

Abstract

We study cyclic codes of length 2p s over \(\mathbb {F}_{q}\), where p is an odd prime. Using the results of [1], we compute the minimum Hamming distance of these codes.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • 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. Castagnoli, G., Massey, J.L., Schoeller, P.A., von Seemann, N.: On repeated-root cyclic codes. IEEE Trans. Inform. Theory 37, 337–342 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  2. Dihn, H.Q.: On the linear ordering of some classes of negacyclic and cyclic codes and their distance distributions. Finite Fields Appl. 14, 22–40 (2008)

    Article  MathSciNet  Google Scholar 

  3. Lidl, R., Niederreiter, H.: Finite Fields. Cambridge University Press, Cambridge (1997)

    MATH  Google Scholar 

  4. MacWilliams, F.J., Sloane, N.J.A.: The Theory Of Error Correcting Codes. North Holland, Amsterdam (1978)

    MATH  Google Scholar 

  5. Özadam, H., Özbudak, F.: A note on negacyclic and cyclic codes of length p s over a finite field of characteristic p (2009) (submitted)

    Google Scholar 

  6. Sălăgean, A.: Repeated-root cyclic and negacyclic codes over a finite chain ring. Discrete Appl. Math. 154(2), 413–419 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  7. López-Permouth, S.R., Szabo, S.: On the Hamming weight of repeated-root cyclic and negacyclic codes over Galois rings (2009) (preprint)

    Google Scholar 

  8. van Lint, J.H.: Repeated-root cyclic codes. IEEE Trans. Inform. Theory 37, 343–345 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  9. Zimmerman, K.-H.: On generalizations of repeated-root cyclic codes. IEEE Trans. Inform. Theory 42, 641–649 (1996)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Özadam, H., Özbudak, F. (2009). The Minimum Hamming Distance of Cyclic Codes of Length 2p s . In: Bras-Amorós, M., Høholdt, T. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2009. Lecture Notes in Computer Science, vol 5527. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02181-7_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-02181-7_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02180-0

  • Online ISBN: 978-3-642-02181-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics