Z-Complementary Code Sets With Flexible Lengths From Generalized Boolean Functions

In this paper, new direct constructions of Z-complementary code sets (ZCCSs) from generalized Boolean functions are proposed. In the literature, most ZCCS constructions based on generalized Boolean functions lead to sequences of power-of-two length. In this study, we show that our proposed methods result in ZCCSs of both power-of-two length and non-power-of-two length. Since the monomials of degrees more than 2 are employed in the proposed constructions, more ZCCSs can be obtained. The constructed ZCCSs admit the theoretical upper bound on the size for a ZCCS when the sequence length is a power of two. Also, the corresponding peak-to-average-power ratio (PAPR) is theoretically upper-bounded when a sequence in the set is used in OFDM. The proposed constructions extend the applications of ZCCSs in practical communication systems, e.g., multicarrier CDMA (MC-CDMA) system, by offering flexible sequence lengths, various set sizes, and bounded PAPR. For example, only one percent of sequences in the constructed ZCCS of size 16 and of length 128 have PAPRs larger than 8 whereas the theoretical upper bound is 16.