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Some communication systems require sets of signals with impulse-like autocorrelation functions and small cross correlation. There is considerable literature on signals with impulse-like autocorrelation functions hut little on sets of signals with small cross correlation. A possible reason is that designers put too severe a restriction on cross correlation magnitudes. This correspondence establishes lower bounds on how small the cross correlation and autocorrelation can simultaneously be.
L. R. Welch (Wed,) studied this question.