Abstract
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 q ⩾ q 0 ( n ), the upper bound qs is established. It is shown that equality holds only for transversal matroid designs.
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