A New Construction of Optimal Symmetrical ZCCS
Rajen Kumar, Prashant Kumar Srivastava, Sudhan Majhi
TL;DR
The paper addresses constructing $2$D perfect arrays, CCCs, and multiple CCCs that realize optimal symmetrical $Z$-complementary code sets (SZCCS) with large set sizes and controlled ZCZ properties. The authors introduce two constructions: a multiplication-matrix based method that yields a $(M,M)$-CCC and a 2D perfect array, and a mutually orthogonal sequence based method that extends to $(M,PN)$-CCC and MCCC while preserving SZCCS correlations. They prove that the assembled families are Golay-complementary and inter-set zero-correlation within a designated ZCZ, culminating in an optimal $(PM,M,PN,N-1)$-SZCCS. The results provide flexible, scalable code constructions that work for arbitrary seed $(M,N)$-CCC and non-prime-power sizes, with practical relevance to MC-CDMA and related high-dimensional signaling systems.
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.