Helleseth, Tor ; Vijay Kumar, P. ; Shanbhag, Abhijit (1996) Codes with the same weight distributions as the Goethals codes and the Delsarte-Goethals codes Designs, Codes and Cryptography, 9 (3). pp. 257-266. ISSN 0925-1022
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Official URL: https://link.springer.com/article/10.1023/A%3A1027...
Related URL: http://dx.doi.org/10.1023/A:1027376421176
Abstract
The Goethals code is a binary nonlinear code of length 2m+1 which has ζp codewords and minimum Hamming distance 8 for any odd m≥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 Z4 of length 2m and Lee distance 8. The Gray map of the dual of the corresponding Z4 code is a Delsarte-Goethals code. We construct codes over Z4 such that their Gray maps lead to codes with the same weight distribution as the Goethals codes and the Delsarte-Goethals codes.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Springer Verlag. |
| Keywords: | Z4-Linear Codes; Goethals Code; Delsarte-Goethals Code |
| ID Code: | 110188 |
| Deposited On: | 31 Jan 2018 10:15 |
| Last Modified: | 31 Jan 2018 10:15 |
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