Nearly all previous analytical results on the performance of direct-sequence spread-spectrum multiple-access (DS/SSMA) communication systems are restricted to systems in which the periodpof the signature sequence is equal to the numberNof chips per data symbol. In many applications, however, it is necessary to employ signature sequences whose periodpis much larger thanN. Thus, successiveN-chip segments of the signature sequence are used to phase-code the carrier during the transmission of successive data symbols. The performance of such systems depends on the partial correlation properties of the signature sequences (rather than the aperiodic correlation properties as in the case whenN=p). In this paper, we consider the performance of a DS/SSMA system for arbitrary values ofpandN. As special cases of our results, we delermine the effects of partial correlation in three classes of systems: those for whichN =p, those for whichNandpare relatively prime, and those for whichNis a divisor ofp. We also provide two methods for the design of sequences for systems for whichNis a divisor ofp.