Some constructions of superimposed codes in Euclidean spaces
Discrete Applied Mathematics - Special issue: International workshop on coding and cryptography (WCC 2001)
Weighted superimposed codes and constrained integer compressed sensing
IEEE Transactions on Information Theory
Lower bounds for sparse recovery
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
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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