Construction of Optimal Binary Z-Complementary Code Sets with New Lengths

TL;DR

This paper introduces three new methods for constructing optimal binary Z-complementary code sets with various lengths, expanding the range of available code parameters for interference-free communication in MC-CDMA systems.

Contribution

The paper presents three novel constructions of optimal binary ZCCSs using generalized Boolean functions, covering new lengths and larger set sizes not previously reported.

Findings

Proposed ZCCSs cover many unreported lengths.

Constructed ZCCSs achieve optimal correlation properties.

Methods enable larger code sets for improved MC-CDMA performance.

Abstract

Z-complementary code sets (ZCCSs) are used in multicarrier code-division multiple access (MC-CDMA) systems, for interference-free communication over multiuser and quasi-asynchronous environments. In this letter, we propose three new constructions of optimal binary $\left(R2^{k+1},2^{k+1}, R\gamma,\gamma\right)$-ZCCS, $\left(R2^{k+1},2^{k+1}, R2^{m_{2}},2^{m_{2}}\right)$-ZCCS and $\left(2^{k+1},2^{k+1},3\gamma,2\gamma\right)$-ZCCS based on generalized Boolean functions (GBFs), where $\gamma=2^{m_{1}-1}+2^{m_{1}-3}, m_{1}\geq 5, k\geq 1,m_{2}\geq 1$ and $R$ is any even number. The proposed ZCCSs cover many unreported lengths and large set sizes.