An Improved Upper Bound of the Rate of Eucledian Superimposed Codes

A family of n-dimensional unit norm vectors is a Euclidean superimposed code, if the sums of any two distinct at most m-tuples of vectors are separated by a certain minimum Euclidean distance d. Ericson and Gyorfi [8] proved that the rate of such a code is between (log m)=4m and (log m)=m for m large enough. In this paper -- improving the above longstanding best upper bound for the rate -- it is shown that the rate is always at most (log m)=2m, i.e., the size of a possible superimposed code is at most the root of the size given in [8]. We also generalize these codes to other normed vector spaces