Novel Constructions of 2-D Golay Complementary Array Sets of Flexible Sizes

Abstract

One-dimensional (1-D) Golay complementary sets(GCSs) possess numerous well-known properties and have achieved extensive use in communication engineering. The concept of 1-D GCSs can be extended to two-dimensional (2-D) Golay complementary array sets(GCASs). The letter proposes two constructions of 2-D GCASs based on two-dimensional extended generalized Boolean functions, where the set sizes and matrix parameters are flexible. The set size of GCASs with an array size of b^m b^n in the letter can reach N^m+n+1, which has not been cited in the existing literature. Both structures are assembled directly and are not restricted by the parameters of other existing sequences, thus expanding the theoretical and applicative boundaries of Golay complementary array sets.