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 complete complementary codes (CCCs) over $\mathbb{Z}_N$, where $N~(N\geq 3)$ is a positive integer of the form $N=p_0^{e^0}p_1^{e^1}\dots p_{n-1}^{e^{n-1}}$, $p_0<p_1<\cdots<p_{n-1}$ are prime factors of $N$ and $e_0,e_1,\cdots,e_{n-1}$ are non-negative integers. Interestingly, the maximum inter-set aperiodic cross-correlation magnitude of the proposed CCCs is upper bounded by $N$. When $N$ is odd, the combination of the proposed CCCs results to a new set of sequences to obtain asymptotically optimal and near-optimal aperiodic quasi-complementary sequence sets (QCSSs) with more flexible parameters.