Asymptotically optimal aperiodic quasi-complementary sequence sets based on extended Boolean functions

Quasi-complementary sequence sets (QCSSs) are important in modern communication systems as they are capable of supporting more users, which is desired in applications like MC-CDMA nowadays. Although several constructions of aperiodic QCSSs have been proposed in the literature, the known optimal aperiodic QCSSs have limited length or have large alphabet. In this paper, based on extended Boolean functions, we present two constructions of aperiodic QCSSs with parameters \((q(p_0-1),q,q-t,q)\) $(q(p_0-1),q,q-t,q)$ and \((q^m(p_0-1),q^m,q^m-t,q^m)\) $(q^m(p_0-1),q^m,q^m-t,q^m)$ , where \(q\ge 3\) $q\ge 3$ is an odd integer, \(p_0\) $p_0$ is the minimum prime factor of q. The proposed constructions can generate asymptotically optimal or near-optimal aperiodic QCSSs with new parameters.