Sequence families with zero or low correlation zone can be used in the quasi-synchronous codedivision 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

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... en, and L ≡ P/2 (mod P ). The conditions are derived under which the new construction is optimal. Some examples are also given to specify the new construction. Index Terms. Quasi-synchronous code-division multiple access (QS-CDMA), low correlation zone (LCZ) sequence, zero correlation zone (LCZ) sequence, interleaving technique.