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

Published 9 Jan 2023 in cs.IT and math.IT | (2301.03294v2)

Abstract: 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.