A Direct Construction of Optimal 2D-ZCACS with Flexible Array Size and Large Set Size

TL;DR

This paper introduces a new method for directly constructing optimal 2D-ZCACS using multivariable functions, enabling flexible array sizes and larger sets, with the ability to convert to 1D-ZCCS, improving on prior methods.

Contribution

The paper presents a novel direct construction technique for 2D-ZCACS with flexible sizes and large sets, also capable of generating 1D-ZCCS, unifying and extending previous designs.

Findings

Constructed 2D-ZCACS with flexible array sizes.

Achieved larger set sizes compared to existing methods.

Demonstrated conversion to 1D-ZCCS.

Abstract

In this paper, we propose a direct construction of optimal two-dimensional Z-complementary array code sets (2D-ZCACS) using multivariable functions (MVFs). In contrast to earlier works, the proposed construction allows for a flexible array size and a large set size. Additionally, the proposed design can be transformed into a one-dimensional Z-complementary code set (1D-ZCCS). Many of the 1D-ZCCS described in the literature appeared to be special cases of this proposed construction. At last, we compare our work with the current state of the art and then draw our conclusions.