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

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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.

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References

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Victoria, P.O. Box 3055, STN CSC, Victoria, B.C, V8W 3P6, Canada

    T. Aaron Gulliver

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

    Masaaki Harada & Takuji Nishimura

  3. Department of Electrical and Communications Engineering, Helsinki University of Technology, P.O. Box 3000, 02015, HUT, Finland

    Patric R. J. Östergård

Authors
  1. T. Aaron Gulliver
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  2. Masaaki Harada
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  3. Takuji Nishimura
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  4. Patric R. J. Östergård
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Corresponding author

Correspondence to T. Aaron Gulliver.

Additional information

Communicated by: P. Fitzpatrick

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Gulliver, T.A., Harada, M., Nishimura, T. et al. Near-Extremal Formally Self-Dual Even Codes of Lengths 24 and 32. Des Codes Crypt 37, 465–471 (2005). https://doi.org/10.1007/s10623-004-4037-6

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  • DOI: https://doi.org/10.1007/s10623-004-4037-6

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