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In this paper, some codes are designed for a binary chip-asynchronous CDMA system which guarantee errorless communication in the absence of noise. These codes also show good performance for noisy channels. In addition, lower and upper bounds for the sum channel capacity are derived for finite and asymptotic cases with the assumption of both noiseless and noisy channels. The results are derived assuming that user delays are known at the receiver end. The performance of proposed codes in the noisy case is also compared to both Gold sequences and a similar class of binary sequences with constrained amount of correlation.