A direct construction of cross z-complementary sequence sets with large set size

Abstract

This paper presents a direct construction of novel type cross Z-complementary sequence sets (CZCSSs), whose aperiodic correlation sums exhibit zero correlation zones at both the front-end and tail-end shifts. CZCSS can be regarded as an extension of the symmetrical Z-complementary code set (SZCCS). The available construction of SZCCS has a limitation on the set size, with a maximum set size of 8. The proposed generalized Boolean function-based construction can generate CZCSS/SZCCS of length in the form of a non-power-of-two with variable set size \(2^{n+1}\), where each code has \(2^{n+1}\) constituent sequences. The proposed construction also yields cross Z-complementary pairs and cross Z-complementary sets with a larger number of constituent sequences compared to the existing work.