## AbstractRandom projections in the Euclidean space reduce the dimensionality of the data approximately preserving the distances between points. In the hypercube it holds a weaker property: random projections approximately preserve the distances within a certain range. In this note, we show an analogous result for the metric space <Sigma^d, d_H>, where Sigma^d is the set of words of length d on alphabet Sigma and d_H is the Hamming distance.
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