A Direct Construction of Cross Z-Complementary Sequence Sets with Large Set Size

TL;DR

This paper introduces a direct method to construct cross Z-complementary sequence sets with large set sizes and flexible lengths, extending existing code sets and overcoming previous size limitations.

Contribution

It proposes a generalized Boolean function based construction for CZCSSs with variable sizes and lengths, surpassing the maximum size of existing SZCCS constructions.

Findings

Constructs CZCSSs with set size $2^{n+1}$ and length not limited to powers of two.

Generates cross Z-complementary pairs and sets with larger constituent sequence numbers.

Overcomes the size limitations of previous SZCCCS constructions.

Abstract

This letter presents a direct construction of 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 of length in the form of 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 large number of constituent sequences compared to the existing work.