Construction of New Optimal Z-Complementary Code Sets from Z-Paraunitary Matrices

Abstract

In this paper, we first introduce a novel concept, called Z-paraunitary (ZPU) matrices. These ZPU matrices include conventional PU matrices as a special case. Then, we show that there exists an equivalence between a ZPU matrix and a Z-complementary code set (ZCCS) when the latter is expressed as a matrix with polynomial entries. The proposed ZPU matrix has an advantage over the conventional PU matrix with regard to the availability of wider range of matrix sizes and sequence lengths. In addition, the proposed construction framework can accommodate more choices of ZCCS parameters compared to the existing works.