On q-ary superimposed codes

We introduce the concept of q-ary superimposed codes. These codes are to be used in a multi-user concept where the set of active users is small compared to the total amount of potential users. The active transmitters use signatures of length n of q-ary symbols to be transmitted over a common channel and the channel output is equal to the set of active input values. We give bounds on the cardinality of the class of signatures as a function of the length n and the number of active users. Furthermore, we construct a class of codes that can be used to uniquely determine the set of active users from the composite signature at the channel output