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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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