Superimposed codes in Rn

The authors introduce the concept of superimposed codes in Euclidean n-space Rⁿ. An asymptotic existence bound is derived for such codes; the proof uses the idea of random coding. In particular, the asymptotic properties of long codes are studied. It is shown that the derived existence bound differs only by a factor of four from a nonexistence bound obtained by a simple sphere-packing argument