Two-Dimensional Binary Z-Complementary Array Pairs

Cheng Yu Pai, Yong Ting Ni, Chao Yu Chen

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


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.

Original languageEnglish
Article number9328523
Pages (from-to)3892-3904
Number of pages13
JournalIEEE Transactions on Information Theory
Issue number6
Publication statusPublished - 2021 Jun

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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