A Novel Construction of Two-Dimensional Z-Complementary Array Code Sets Based on Extended Boolean Functions

Two-dimensional (2-D) array sets with good 2-D correlation properties have received considerable attention in wireless communication systems. This paper focuses on 2-D Z-complementary array code sets (ZCACSs), which have ideal 2-D correlation properties within a rectangular zone around the origin. By developing a theory linking 2-D extended Boolean functions with 2-D arrays, we establish an efficient construction of 2-D ZCACSs. In contrast to previous work, the proposed construction is capable of producing 2-D ZCACSs with new flexible parameters. Constructions of three-dimensional (3-D) and higher-dimensional ZCACSs are further investigated. We remark that 2-D and higher-dimensional complete complementary codes (CCCs) can also be generated from the proposed constructions.