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The merits of phase-coherent communications are widely recognized for both discrete and continuous modulation systems -. The relative performances of phase-coherent and noncoherent transmission of binary data in the presence of additive white Gaussian noise have been analyzed and compared  and . This paper considers the result of encoding independent equiprobable binary words or sequences of independent binary digits into sets of binary code words. These are transmitted over a channel perturbed by additive white Gaussian noise and detected by correlating them with their stored or locally generated replicas at the receiver. The word error probabilities and bit error probabilities for low cross-correlation codes are determined as a function of the ratio (received signal energy)/bit/(noise power)/(unit bandwidth) The received information rate and the potential channel capacity are also computed. It is shown that in the limit as the code word length and the bandwidth approach infinity, the received information rate approaches the channel capacity for only one value of the above ratio.