Mutually orthogonal complementary sets (MOCSs) have received significant research attention in recent years due to their wide applications in communications and radar. Existing MOCSs which are constructed based on generalized Boolean functions (GBFs) mostly have lengths of power-of-two. How to construct MOCSs with non-power-of-two lengths whilst having large set sizes is a largely open problem. With the aid of GBFs, in this paper, we present new constructions of such MOCSs and show that the maximal achievable set size is 1/2 of the flock size of an MOCS.

In this paper, a new direct construction of zero correlation zone complementary sequence sets (ZCZ- CSs) via generalized Boolean functions is proposed. The resultant ZCZ-CSs can meet the theoretical upper bound on the set size and have good peak-to-average power ratios (PAPRs). Boolean monomials of degrees more than 2 are considered in our construction, so more ZCZ-CSs can be obtained. The larger number of ZCZ-CSs constructed by our method will increase possible applications in practical communication systems.

In this letter, a novel construction of Z-complementary sequence (ZCS) sets is proposed based on generalized Boolean functions. The constructed ZCS set is optimal since the set size achieves the theoretical upper bound. In addition, the proposed construction is a direct construction without the aid of other special sequences. In this letter, the peak-to-average power ratio (PAPR) property of the constructed ZCS sets is also investigated. Furthermore, the set sizes, flock sizes, sequence lengths, and the widths of zero correlation zones of the constructed ZCS sets are all very flexible.

Zero correlation zone (ZCZ) sequence sets and Golay complementary sets (GCSs) have different correlation properties and hence have different engineering applications. A number of constructions of ZCZ sequence sets and GCSs have been proposed, respectively, in the literature. In addition, some ZCZ sequence sets can be constructed from mutually orthogonal GCSs. In this paper, the relationship between GCSs and ZCZ sets is discovered further. We propose a new type of sequence sets which are ZCZ sequence sets and also GCSs. They are called the Golay-ZCZ sequence sets in this paper. Therefore, they have low peak-to-average power ratios when employed in OFDM systems due to the good autocorrelation properties of GCSs. Besides, the Golay-ZCZ sets possess zero autocorrelations and cross-correlations within their ZCZ and hence have the potential application to synchronization. Furthermore, a construction of Golay-ZCZ sequence family with flexible set sizes, various sequence lengths, and large ZCZ widths is proposed in this paper.