An improved upper bound of the rate of Euclidean superimposed codes

A family of n-dimensional unit norm vectors is an Euclidean superimposed co de if the sums of any two distinct at most m-tuples of vectors are separate d 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)lm for m larg e 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 gi ven in [8]. We also generalize these codes to other normed vector spaces.