Skip to main content
SpringerLink
Log in

On the Classification of Self-dual -Codes

  • Conference paper
Cryptography and Coding (IMACC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 5921))

Included in the following conference series:

Abstract

A classification of self-dual -codes of modest lengths is known for small k. For k = 4,6,8,9 and 10, the classification of self-dual -codes is extended to lengths 19,12,12,12 and 10, respectively, by considering k-frames of unimodular lattices.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Balmaceda, J.M.P., Betty, R.A.L., Nemenzo, F.R.: Mass formula for self-dual codes over \({\mathbf Z}_{p^2}\). Discrete Math. 308, 2984–3002 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bannai, E., Dougherty, S.T., Harada, M., Oura, M.: Type II codes, even unimodular lattices, and invariant rings. IEEE Trans. Inform. Theory 45, 1194–1205 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  3. Betsumiya, K., Betty, R.A.L., Munemasa, A.: Mass formula for even codes over Z 8. In: Parker, M.G. (ed.) IMACC 2009. LNCS, vol. 5921, pp. 65–77. Springer, Heidelberg (2009)

    Google Scholar 

  4. Bosma, W., Cannon, J.: Handbook of Magma Functions. Department of Mathematics, University of Sydney, http://magma.maths.usyd.edu.au/magma/

  5. Conway, J.H., Sloane, N.J.A.: Self-dual codes over the integers modulo 4. J. Combin. Theory Ser. A 62, 30–45 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  6. Conway, J.H., Sloane, N.J.A.: Sphere Packing, Lattices and Groups, 3rd edn. Springer, New York (1999)

    Google Scholar 

  7. Dougherty, S.T., Gulliver, T.A., Wong, J.: Self-dual codes over and . Des. Codes Cryptogr. 41, 235–249 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  8. Dougherty, S.T., Harada, M., Solé, P.: Self-dual codes over rings and the Chinese remainder theorem. Hokkaido Math. J. 28, 253–283 (1999)

    MATH  MathSciNet  Google Scholar 

  9. Fields, J., Gaborit, P., Leon, J.S., Pless, V.: All self-dual codes of length 15 or less are known. IEEE Trans. Inform. Theory 44, 311–322 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  10. Gaborit, P.: Mass formulas for self-dual codes over \(Z\sb 4\) and \(F\sb q+uF\sb q\) rings. IEEE Trans. Inform. Theory 42, 1222–1228 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  11. Harada, M., Munemasa, A.: Database of Self-Dual Codes, http://www.math.is.tohoku.ac.jp/~munemasa/selfdualcodes.htm

  12. Harada, M., Munemasa, A., Venkov, B.: Classification of ternary extremal self-dual codes of length 28. Math. Comput. 78, 1787–1796 (2009)

    MathSciNet  Google Scholar 

  13. Kitazume, M., Ooi, T.: Classification of type II \(Z\sb 6\)-codes of length 8. AKCE Int. J. Graphs Comb. 1, 35–40 (2004)

    MATH  MathSciNet  Google Scholar 

  14. Nagata, K., Nemenzo, F., Wada, H.: The number of self-dual codes over \({\mathbf Z}_{p^3}\). Des. Codes Cryptogr. 50, 291–303 (2009)

    Article  MathSciNet  Google Scholar 

  15. Park, Y.H.: Modular independence and generator matrices for codes over . Des. Codes Cryptogr. 50, 147–162 (2009)

    Article  MathSciNet  Google Scholar 

  16. Pless, V., Leon, J.S., Fields, J.: All codes of Type II and length 16 are known. J. Combin. Theory Ser. A 78, 32–50 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  17. Rains, E.: Optimal self-dual codes over . Discrete Math. 203, 215–228 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  18. Rains, E., Sloane, N.J.A.: Self-Dual Codes: Handbook of Coding Theory. In: Pless, V.S., Huffman, W.C. (eds.), pp. 177–294. Elsevier, Amsterdam (1998)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Yamagata University, Yamagata, 990–8560, Japan

    Masaaki Harada

  2. PRESTO, Japan Science and Technology Agency, Kawaguchi, Saitama, 332–0012, Japan

    Masaaki Harada

  3. Graduate School of Information Sciences, Tohoku University, Sendai, 980–8579, Japan

    Akihiro Munemasa

Authors
  1. Masaaki Harada
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Akihiro Munemasa
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. The Selmer Centre Department of Informatics, University of Bergen, P.O. Box 7800, N-5020, Bergen, Norway

    Matthew G. Parker

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Harada, M., Munemasa, A. (2009). On the Classification of Self-dual -Codes. In: Parker, M.G. (eds) Cryptography and Coding. IMACC 2009. Lecture Notes in Computer Science, vol 5921. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10868-6_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-10868-6_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10867-9

  • Online ISBN: 978-3-642-10868-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation