An improved upper bound of the rate of Euclidean superimposed codes

A family of n-dimensional unit norm vectors is an 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 (1988) 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 long-standing 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 by Ericson et al. We also generalize these codes to other normed vector spaces.