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The recently proposed loosely synchronized (LS) spreading code can in principle realize an intracell-interference-free quasi-synchronous code-division multiple-access (QS-CDMA) system by creating a wide enough interference-free window (IFW). However, the problem of minimizing intercell interference (ICI) in a cellular QS-CDMA system remains an open issue. Addressing the problem from a sequence design viewpoint, the key challenge is how to generalize the known construction of a single LS code to the design of many families of generalized LS (GLS) codes so that a desirable code family can be selected for the realization of a low-ICI cellular QS-CDMA system. Our main contribution is a systematic construction of new families of GLS codes with favorable intercode cross-correlation properties within a certain window, while maintaining the desirable IFW property. Many such code families can be obtained …