A Direct Construction of Cross Z-Complementary Sets with Flexible Lengths and Large Zero Correlation Zone

Abstract

This letter proposes a direct construction for cross Z-complementary sets (CZCSs) with flexible lengths and a large zero correlation zone (ZCZ). CZCS is an extension of the cross Z-complementary pair (CZCP). The maximum possible ZCZ width of a CZCP is half of its sequence length. In this letter, for the first time, a generalized Boolean function based construction of CZCSs with a large number of constituent sequences and a ZCZ ratio of $2/3$ is presented. For integers $m$ and $\delta$, the proposed construction produces CZCS with length expressed as $2^{m-1}+2^\delta$ ($0 \leq \delta <m-1,m\geq 4$), where both odd and even lengths CZCS can be obtained. Additionally, the constructed CZCS also feature a complementary set of the same length. Finally, the proposed construction is compared with the existing works.