Z-complementary code sets (ZCCSs) are used in multicarrier code-division multiple access (MC-CDMA) systems, for interference-free communication over multiuser and quasi-asynchronous environments. In this letter, we propose three new constructions of optimal binary $\left(R2^{k+1},2^{k+1}, R\gamma,\gamma\right)$-ZCCS, $\left(R2^{k+1},2^{k+1}, R2^{m_{2}},2^{m_{2}}\right)$-ZCCS and $\left(2^{k+1},2^{k+1},3\gamma,2\gamma\right)$-ZCCS based on generalized Boolean functions (GBFs), where $\gamma=2^{m_{1}-1}+2^{m_{1}-3}, m_{1}\geq 5, k\geq 1,m_{2}\geq 1$ and $R$ is any even number. The proposed ZCCSs cover many unreported lengths and large set sizes.

翻译：Z互补码集（ZCCSs）用于多载波码分多址（MC-CDMA）系统，可在多用户和准异步环境下实现无干扰通信。本文基于广义布尔函数（GBFs）提出了三种最优二元码集的新构造方法：$\left(R2^{k+1},2^{k+1}, R\gamma,\gamma\right)$-ZCCS、$\left(R2^{k+1},2^{k+1}, R2^{m_{2}},2^{m_{2}}\right)$-ZCCS和$\left(2^{k+1},2^{k+1},3\gamma,2\gamma\right)$-ZCCS，其中$\gamma=2^{m_{1}-1}+2^{m_{1}-3}$，$m_{1}\geq 5$，$k\geq 1$，$m_{2}\geq 1$，且$R$为任意偶数。所提ZCCS涵盖了多种此前未报道的长度和较大集合规模。