In this paper, we constructed a class of low correlation zone sequence sets derived from the interleaved technique and DFT matrices. When p is a prime such that p>3, p-ary LCZ sequence sets with parameters LCZ(pⁿ-1,p^m-1,(pⁿ-1)/(p^m-1),1) are constructed based on a DFT matrix with order p×p, which is optimal with respect to the Tang-Fan-Matsufuji bound. When p is a prime such that p≥2, p^k-ary LCZ sequence sets with parameters LCZ(pⁿ-1,p^k-1,(pⁿ-1)/(p^k-1),1) are constructed based on a DFT matrix with order p^k×p^k, which is also optimal. These sequence sets are useful in certain quasi-synchronous code-division mutiple access (QS-CDMA) communication systems.