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 $\left(R2^{k+1},2^{k+1}, Rγ,γ\right)$-ZCCS, $\left(R2^{k+1},2^{k+1}, R2^{m_{2}},2^{m_{2}}\right)$-ZCCS and $\left(2^{k+1},2^{k+1},3γ,2γ\right)$-ZCCS based on generalized Boolean functions (GBFs), where $γ=2^{m_{1}-1}+2^{m_{1}-3}, m_{1}\geq 5, k\geq 1,m_{2}\geq 1$ and $R$ is any even number. The proposed ZCCSs cover many unreported lengths and large set sizes.