Constructions of golay complementary (array) sets based on extended boolean functions

In this paper, we propose a direct construction of Golay complementary sets (GCSs) with flexible length $ aq^m $ for set size $ q^{k} $ using extended Boolean functions (EBFs), where $ a $ and $ q $ are positive integers with $ a\leq q $. As an extension of GCSs, we also propose two-dimensional (2-D) Golay complementary array sets (GCASs) using 2-D EBFs. The parameters of the proposed GCASs are more flexible as compared to the previous works.