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Designs, Codes and Cryptography

, Volume 37, Issue 3, pp 465–471 | Cite as

Near-Extremal Formally Self-Dual Even Codes of Lengths 24 and 32

  • T. Aaron GulliverEmail author
  • Masaaki Harada
  • Takuji Nishimura
  • Patric R. J. Östergård
Article

Abstract

The weight enumerator of a formally self-dual even code is obtained by the Gleason theorem. Recently, Kim and Pless gave some restrictions on the possible weight enumerators of near-extremal formally self-dual even codes of length divisible by eight. In this paper, the weight enumerators for which there is a near-extremal formally self-dual even code are completely determined for lengths 24 and 32, by constructing new near-extremal formally self-dual codes. We also give a classification of near- extremal double circulant codes of lengths 24 and 32.

Keywords

Formally self-dual even codes weight enumerators 

AMS classification

94B05 

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References

  1. Betsumiya, K., Harada, M. 2001Classification of formally self-dual even codes of lengths up to 16Des. Codes. Cryptogr23325332CrossRefGoogle Scholar
  2. Gulliver, T.A., Harada, M. 1997Classification of extremal double circulant formally self-dual even codesDes. Codes. Cryptogr112535CrossRefGoogle Scholar
  3. Harada, M., Östergård, P.R.J 2002Classification of extremal formally self-dual even codes of length 22Graphs Combin18507516CrossRefGoogle Scholar
  4. J.-L. Kim and V. Pless, A note on formally self-dual even codes of length divisible by 8, preprint.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • T. Aaron Gulliver
    • 1
    Email author
  • Masaaki Harada
    • 2
  • Takuji Nishimura
    • 2
  • Patric R. J. Östergård
    • 3
  1. 1.Department of Electrical and Computer EngineeringUniversity of VictoriaVictoriaCanada
  2. 2.Department of Mathematical SciencesYamagata UniversityYamagataJapan
  3. 3.Department of Electrical and Communications EngineeringHelsinki University of TechnologyHUTFinland

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