Three New Constructions of Asymptotically Optimal Periodic Quasi-Complementary Sequence Sets With Small Alphabet Sizes

Quasi-complementary sequence sets (QCSSs) play an important role in multi-carrier code-division multiple-access (MC-CDMA) systems. They can support more users than perfect complementary MC-CDMA It is desirable to design QCSSs with good parameters that are a trade-off of large set size, small periodic maximum magnitude correlation and alphabet size. The main results construct new infinite families all have size asymptotically optimal correlation. In this paper, we propose three constructions using additive characters over finite fields. Notably, these sizes. Using the properties character sums, determine their magnitudes prove respect lower bound.