A New Construction of Optimal Symmetrical ZCCS

TL;DR

This paper introduces new methods for constructing optimal symmetrical Z-complementary code sets (ZCCS) using two-dimensional arrays and mutually orthogonal sequences, enhancing code length and supporting multiple CCCs.

Contribution

It presents novel constructions for 2D perfect arrays, CCC, and multiple CCCs, with a method to extend code length without increasing set size, maintaining optimal correlation properties.

Findings

Developed a method to generate 2D perfect arrays and CCCs.

Extended CCC length using mutually orthogonal sequences.

Achieved multiple CCCs with correlation characteristics matching optimal symmetrical ZCCS.

Abstract

We propose new constructions for a two-dimensional ($2$D) perfect array, complete complementary code (CCC), and multiple CCCs as an optimal symmetrical $Z$-complementary code set (ZCCS). We propose a method to generate a two-dimensional perfect array and CCC. By utilising mutually orthogonal sequences, we developed a method to extend the length of a CCC without affecting the set or code size. Additionally, this concept is extended to include the development of multiple CCCs, and the correlation characteristics of these multiple CCCs are identical with the characteristics of optimal symmetrical ZCCS.