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Translates of linear codes over \(\mathbb{Z}_ 4\). (English) Zbl 0885.94028
General techniques for studying the complete coset weight distributions of quaternary codes are derived and applied to quaternary Kerdock codes and Preparata codes. These two classes of codes have ten distinct complete coset weight enumerators, independently of the code length.
The determination of the coset weight enumerators having been solved for few families of codes and allowing the calculation of precise probabilities of correct error-correction, the results contained in this paper are quite interesting. In the cases studied here, they are also related to exponential sums.

MSC:
94B05 Linear codes, general
11T23 Exponential sums
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