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An improved upper bound of the rate of Euclidean superimposed codes

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2 Author(s)
Furedi, Z. ; Dept. of Math., Illinois Univ., Urbana, IL, USA ; Ruszinko, M.

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

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Information Theory, IEEE Transactions on  (Volume:45 ,  Issue: 2 )