The class of complete complementary sequences (of fixed length) have the ideal correlation properties and are good at increasing the channel usage efficiency but lacks in desirable sequence lengths. In spread spectrum communication systems, sequences having nice correlation properties are important in many ways such as in suppressing multi-user interference, for reliable initial synchronization and in separation of the multipath components. It would be even good if the sequences are easy to construct and have desirable lengths for the system under consideration. In this paper, M sets of sequences that constitute a complete complementary sequences with ith set containing N sequences of length Li each, i = 0, 1, ..., M - 1, is defined and a general method that constructs such a class of complete complementary sequences (of different lengths) is given. The proposed class of complete complementary sequences, constituted by sequence sets of different lengths, does not increase the data rates when short-length sequences are employed.

Large Area Synchronized (LAS)-CDMA, actually composed of LA codes and pulse compressing LS codes, has been proposed as a most promising scheme in 3G and 4G wireless communications. LS codes are famous for the Zero Correlation Zone (ZCZ) in the auto-correlation and cross-correlation functions, which endows the codes with the capability to perfectly reduce the Multiple Access Interference (MAI) and Inter Symbol Interference (ISI) if the maximum transmission delay is less than the length of ZCZ. In this letter, we provide a general and systematic method to construct LS codes from the set of complete complementary sequences. Our method is much more general than the ordinary LS construction method revealed previously.