Superimposed codes for multiple-access communication in a binary adder channel are analyzed. The superposition mechanism used in this correspondence is ordinary addition. Each user is assigned a codeword from a superimposed code. It is proved that every constant-weight code C of weight w and maximal correlation c corresponds to a subclass of a disjunctive code D of order m<w/c. Therefore, any m or less codewords in C which are used at the same time yield a uniquely decodable code combination at the output of the adder channel. In the noisy case, for each subset A⊆C of size |A|⩽m≪T the receiver is able to determine the number of active users and to distinguish between the active users if the weight of the error pattern e satisfies Wt(e)<min{w-c|A|, w/2}. Decoding algorithms for both the noiseless and the noisy cases are proposed