• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.8C
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• pp.765-770
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• 2003

In this paper, the complete weight enumerator of the Delsarte-Goethals code over Z$_4$ is obtained. This code is divided into 3 cases and the complete weight enumerator of each case is calculated. During this weight enumeration, the blown distribution of exponential sums and binary weight distribution of the sub-codes are used. By combining this result and MacWilliams identity, the complete weight enumerator of the Goethals code over Z$_4$can be easily obtained. This result is also used for finding 3-designs from the Goethals and Delsarte-Goethals codes over Z$_4$.