Support weight distribution of \(\mathbb Z_4\)-linear codes
The author gives a relation between the support weight distribution of a \(\mathbb{Z}_4\)-linear code of type \(4^k\) and the Hamming weight distribution of the same code considered as a code over the Galois ring \(\text{GR}(4^m)\). Using the MacWilliams identities between dual codes over \(\text{GR}(4^m)\), the author derives a relation between the support weight distribution of the \(\mathbb{Z}_4\)-linear code and its dual. These results are generalizations of similar results due to \textit{T. Kløve} [Discrete Math. 106/107, 311-316 (1992; Zbl 0754.94008)] and \textit{J. Simonis} [Appl. Algebra Eng. Commun. Comput. 5, 371-377 (1994; Zbl 0805.94016)] for the case of codes over finite fields.
scientific article; zbMATH DE number 1746233