Set Size Bound for Aperiodic Z-Complementary Sets

TL;DR

This paper proves a conjectured upper bound on the set size of aperiodic Z-complementary sets and introduces a new construction method using extended generalized Boolean functions, resulting in optimal ZCSs with novel parameters.

Contribution

It provides a proof for the long-standing conjectured upper bound and proposes a new construction method for optimal ZCSs using EGBFs.

Findings

Confirmed the conjectured upper bound on ZCS set size.

Developed a new construction method for ZCSs using EGBFs.

Generated optimal ZCSs with new parameters.

Abstract

The widely and commonly adopted upper bound on the set size of aperiodic Z-complementary sets (ZCSs) in the literature has been a conjecture. In this letter, we provide detailed derivations for this conjectured bound. A ZCS is optimal when its set size reaches the upper bound. Furthermore, we propose a new construction of ZCSs based on extended generalized Boolean functions (EGBFs). The proposed method introduces optimal ZCSs with new parameters.