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Codes with the Same Weight Distributions as the Goethals Codes and the Delsarte-Goethals Codes

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Abstract

The Goethals code is a binary nonlinear code of length 2m+1 which has \(\zeta _p\) codewords and minimum Hamming distance 8 for any odd \(m \geqslant 3\). Recently, Hammons et. al. showed that codes with the same weight distribution can be obtained via the Gray map from a linear code over Z 4of length 2m and Lee distance 8. The Gray map of the dual of the corresponding Z 4 code is a Delsarte-Goethals code. We construct codes over Z 4 such that their Gray maps lead to codes with the same weight distribution as the Goethals codes and the Delsarte-Goethals codes.

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References

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Authors and Affiliations

  1. Department of Informatics, University of Bergen, Hoyteknologisenteret, N-5020, Bergen, Norway

    Tor Helleseth

  2. Communications Sciences Institute, University of Southern California, Los Angeles, CA, 90089-2565, USA

    P. Vijay Kumar

  3. Communications Sciences Institute, University of Southern California, Los Angeles, CA, 90089-2565, USA

    Abhijit Shanbhag

Authors
  1. Tor Helleseth
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  2. P. Vijay Kumar
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  3. Abhijit Shanbhag
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Helleseth, T., Kumar, P.V. & Shanbhag, A. Codes with the Same Weight Distributions as the Goethals Codes and the Delsarte-Goethals Codes. Designs, Codes and Cryptography 9, 257–266 (1996). https://doi.org/10.1023/A:1027376421176

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  • DOI: https://doi.org/10.1023/A:1027376421176

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