New Constructions of Mutually Orthogonal Complementary Sets and Z-Complementary Code Sets Based on Extended Boolean Functions

TL;DR

This paper introduces new direct methods for constructing mutually orthogonal complementary sets and Z-complementary code sets using extended Boolean functions, enabling flexible lengths and optimal set sizes for practical applications.

Contribution

It presents novel direct constructions of MOCSs and ZCCSs based on extended Boolean functions, including flexible and non-power-of-two lengths, and optimal set size generation.

Findings

Constructed MOCSs with flexible, non-power-of-two lengths.

Generated optimal ZCCSs meeting set size bounds.

Methods suitable for rapid hardware implementation.

Abstract

Mutually orthogonal complementary sets (MOCSs) and Z-complementary code sets (ZCCSs) have many applications in practical scenarios such as synthetic aperture imaging systems and multi-carrier code division multiple access (MC-CDMA) systems. With the aid of extended Boolean functions (EBFs), in this paper, we first propose a direct construction of MOCSs with flexible lengths, and then propose a new construction of ZCCSs. The proposed MOCSs cover many existing lengths and have non-power-of-two lengths when q = 2. Our presented second construction can generate optimal ZCCSs meeting the set size upper bound. Note that the proposed two constructions are direct without the aid of any special sequence, which is suitable for rapid hardware generation.