A Generalised Construction of Multiple Complete Complementary Codes and Asymptotically Optimal Aperiodic Quasi-Complementary Sequence Sets

In recent years, complementary sequence sets have found many important applications in multi-carrier code-division multiple-access (MC-CDMA) systems for their good correlation properties. In this paper, we propose a construction, which can generate multiple sets of $(N,N,N)$- complete complementary codes (CCCs) over $\mathbb{Z}_N$, where $N~(N\geq 3)$ is a positive integer of the form $N=pq$ ($p$ is the least prime factor of $N$ and $q$ is an odd integer). Interestingly, the maximum inter-set aperiodic cross-correlation magnitude of the proposed CCCs is bounded by $N$. When $N$ is odd, the combination of the proposed CCCs results to a new set of sequences to obtain asymptotically optimal aperiodic quasi-complementary sequence sets (QCSSs) with parameters $(N(p-1)^2,N,N,N)$, having much greater set size than the set size of the asymptotically optimal and near-optimal QCSSs reported till date, with more flexible parameters.