Upper Bounds for the Cardinality of s-Distances Codes

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The maximum cardinality of a code of length n over an alphabet of size q and with s distinct distances is considered. Generalizing Delsarte's method, some examples and conditions for existence of modular Hadamard codes are given. Also a non-existence theorem for Hadamard codes of index 2 is proved. In the case qq0(n), the upper bound qs is established. It is shown that equality holds only for transversal matroid designs.

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