Asymptotically Optimal Quasi-Complementary Code Sets from Multivariate Functions

Owing to the more significant set size properties as compared to the set of complete complementary codes (CCCs), quasi-complementary code sets (QCCSs) are more convenient to support a large number of users in multicarrier code-division multiple-access (MC-CDMA) system over CCCs. Besides set size, it is also desirable to have a low maximum aperiodic correlation magnitude and small alphabet size. This paper aims to construct asymptotically optimal and near-optimal aperiodic QCCSs having a small alphabet size and low maximum correlation magnitude. Using multivariate functions and its associated graph, we propose a family of QCCSs consisting of multiple sets of CCCs and determine the parameters of the proposed QCCSs. Unlike the existing constructions of aperiodic QCCSs, the proposed construction can maintain a small alphabet size irrespective of the increasing sequence length and large set size.