Mutually orthogonal complementary sets (MOCSs) and Z-complementary code sets (ZCCSs) have many applications in practical scenarios such as synthetic aperture imaging systems and multi-carrier code division multiple access (MC-CDMA) systems. With the aid of extended Boolean functions (EBFs), in this paper, we first propose a direct construction of MOCSs with flexible lengths, and then propose a new construction of ZCCSs. The proposed MOCSs cover many existing lengths and have non-power-of-two lengths when q = 2. Our presented second construction can generate optimal ZCCSs meeting the set size upper bound. Note that the proposed two constructions are direct without the aid of any special sequence, which is suitable for rapid hardware generation.

翻译：相互正交互补集（MOCSs）与Z互补码集（ZCCSs）在合成孔径成像系统和多载波码分多址（MC-CDMA）系统等实际场景中具有广泛应用。本文借助扩展布尔函数（EBFs），首先提出了一种具有灵活长度的MOCS直接构造方法，进而提出了一种新的ZCCS构造方案。所提出的MOCS覆盖了现有多种长度，且在q=2时可生成长度非2的幂的序列。第二种构造方法可生成达到集合规模上界的最优ZCCS。值得注意的是，这两种构造均为直接构造方法，无需借助任何特殊序列，适用于快速硬件生成。