Constructions Of Sequences Via Generalized Cyclclmic And Interleaved Structure

In modern communication systems such as ultrawideband (UWB), military com-munications, Bluetooth and so on, frequency hopping multiple-access (FHMA) is widely used. In these systems we have to use a set of frequency hopping sequences (FHS) to minimize the maximum of Hamming out-of-phase auto-and cross-correlation to discriminate their own signals from the others and reduce multiple-access interfer-ence. It is also desirable that the size of the FHS set is as large as possible to accom-modate a great quantity of users.However, the parameters of the FHS sets are subjected to some theoretic bounds. The Lempel-Greenberger lower bound of Hamming auto-correlation was established by Lempel and Greenberger in1976[59]. In2004[86] Peng and Fan developed the Peng-Fan bounds which take account of the number of sequences in the FHS set. Some other bounds of FHSs from coding theory were also discussed in [31] and [93]. Therefore, it is of great interest to construct optimal FHSs with respect to these bounds. By defining a new generalize cyclotomy, a construction of FHS set, which can generates optimal FHS sets with any odd length lager than3is given in this paper. Two constructions of FHS are given via the generalize cyclotomy.Meanwhile, a construction of Zero-difference balanced (ZDB) functions based on the new generalized cyclotomy is also given, and ZDB functions with new parameters can be generated. As a result, constructions of optimal constant composition codes (CCCs) and optimal and perfect difference systems of sets can be given. Based on the new generalize cyclotomy, we give an construction of optical orthogonal codes, and the generated optical orthogonal codes can be asymptotically optimal.In1995, Gong first introduced the notion of interleaved structure [50]. In this paper, constructions of FHS sets base on the interleaved structure are also given. By applying those constructions recursively many optimal FHS and FHS sets with new parameters can be generated.Families of pseudorandom sequences have wide applications in code-division multiple-access (CDMA) communications. In these applications, sequence families are preferred to have desired properties such as balance property, large family size, long period, low out-of-phase auto-correlation, low cross-correlation, and large lin-ear complexity [49],[56]. Since1960s, many families of binary sequences with good properties have been found. For example, the Gold sequences [5],[48] and Kasami sequences [56],[74],[99]. By obtaining some new shift sequences, we generalize the Gong’s construction which can generates much more sequence families with larger family size, balance property, low correlation.