Two-Dimensional Binary Z-Complementary Array Pairs

One-dimensional (1-D) Golay complementary pair (GCP) and its extension Z-complementary pair (ZCP) with additional zero autocorrelation zone property have been widely studied in the literature. Recently, the investigation of 1-D GCPs have been extended to two-dimensional (2-D) and higher dimensional Golay complementary array pairs (GCAPs). In this article, the concept of zero correlation zone (ZCZ) is applied to 2-D GCAP and the 2-D Z-complementary array pair (ZCAP) is presented. Several constructions of ZCAPs are proposed in this article and the existence of ZCAPs is discussed as well. Based on the proposed constructions, 2-D ZCAPs are shown to exist for all sizes. Furthermore, an upper bound on the rectangular ZCZ size of the 2-D ZCAP is derived when both dimensions are odd. The proposed constructions can include ZCAPs which achieve the upper bound.

Automated summary

The concept of Golay complementary pairs has been extended to two-dimensional arrays with the introduction of zero correlation zone property. Various constructions of Z-complementary array pairs are proposed in the article, along with a discussion on their existence for all sizes. Additionally, an upper bound on the rectangular ZCZ size of the 2-D ZCAP is derived for odd dimensions, with proposed constructions achieving this upper bound.