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Sequence families with zero or low correlation zone can be used in the quasi-synchronous code-division multiple-access (QS-CDMA) communication systems. Interleaving techniques are very useful for sequence design. In this paper, we present a general construction of sequence families with zero or low correlation zone using interleaving techniques and complex Hadamard matrices. The component sequences are perfect or ideal two-level. In two cases, we construct the shift sequences: 1) P|L; 2) P is even, and L Â¿ P/2 ( mod P), which results in sequence families with zero or low correlation zone of parameters (NP, MP, L, PÂ¿), where N is the period of component sequences, M is the number of inequivalent shift sequences, and Â¿ = 0 or 1. The conditions are derived under which the new construction is optimal. Some examples are also given to specify the new construction.