• 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$_4$.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.107-120
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• 2008

There has been a recent growth of interest in codes with respect to a newly defined non-Hamming metric grown as the Rosenbloom-Tsfasman metric (RT, or $\rho$, in short). In this paper, the definitions of the Lee complete $\rho$ weight enumerator and the exact complete $\rho$ weight enumerator of a code over $M_n_\times_s(Z_4)$ are given, and the MacWilliams identities with respect to this RT metric for the two weight enumerators of a linear code over $M_n_\times_s(Z_4)$ are proven too. At last, we also prove that the MacWilliams identities for the Lee and exact complete $\rho$ weight enumerators of a linear code over $M_n_\times_s(Z_4)$ are the generalizations of the MacWilliams identities for the Lee and complete weight enumerators of the corresponding code over $Z_4$.