Construction of Optimal Binary Z-Complementary Code Sets with New Lengths

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 $(R{2}^{k+1},2^{k+1},R\gamma ,\gamma )$-ZCCS, $(R{2}^{k+1},2^{k+1},R{2}^{m_2},2^{m_2})$-ZCCS and $(2^{k+1},2^{k+1},3\gamma ,2\gamma )$-ZCCS based on generalized Boolean functions (GBFs), where $\gamma =2^{m_1-1}+2^{m_1-3},m_1\ge 5,k\ge 1,m_2\ge 1$ and $R$ is any even number. The proposed ZCCSs cover many unreported lengths and large set sizes.