Constructions of Two-Dimensional Golay Complementary Array Pairs Based on Generalized Boolean Functions

The two-dimensional (2-D) Golay complementary array pair (GCAP) is an extension of the one-dimensional (1-D) Golay complementary pair (GCP). The sums of 2-D autocorrelations of constituent arrays of a GCAP are zero except for the 2-D zero shift. In this paper, the 2-D generalized Boolean function is introduced and a novel construction of 2-D GCAPs is proposed based on generalized Boolean functions. Moreover, we provide a construction of 2-D Golay complementary array mate from Boolean functions as well. One potential of 2-D GCAPs is 2-D synchronization.