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A new method for generating families of ternary spreading sequences is presented. The sequences have aperiodic zero correlation zones and large families are created for a specific sequence length. The sequences are proposed as spreading sequences to provide high capacity and cancel multipath and multiple access interference (MAI) in a single carrier (SC) or multicarrier (MC) direct-sequence code division multiple access (DS-CDMA) system. A multicarrier DS-CDMA system is simulated that employs the new sequences as spreading sequences in a multipath channel. Bit error rates (BER) and frame error rates (FER) for a range of Eb/N0 values are presented and it is demonstrated that the proposed sequences improve the BER and FER performance when used in place of masked Walsh codes for the frequency selective fading channel evaluated, when a single correlator receiver is used on each sub-carrier.