A Direct Construction of q-Ary 2-D Z-Complementary Array Pair Based on Generalized Boolean Functions

Two dimensional (2-D) Z-complementary array pair (ZCAP) is a pair of 2-D arrays or matrices, whose 2-D auto-correlation sum gives zero value at all time shifts in a zone around the (0, 0) time shift, except the (0, 0) time shift. The zone is called the zero correlation zone (ZCZ). 2-D ZCAP has found application in 2-D synchronization, phased array antenna, ultra wide band (UWB) systems and so on. To the best of authors' knowledge, most of the constructions of 2-D ZCAPs in the existing literature need special sequences at its intial stage. In this letter, for the first time, we propose a direct construction of 2-D ZCAPs of non-power-of-two sizes, which does not need any special sequence at the initial stage. The construction is based on generalized Boolean function (GBF) and thus facilitates rapid generation for use in several fields.