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The need of two dimensional (2-D) arrays with good 2-D correlation propertieshave been found of great interest in research because of the rapid developmentof the modern technologies in the field of wireless communications. 2-D arrayshave found various applications wireless communication technologies such asultra-wide band (UWB), 2-D synchronization, phased array antenna etc. In thispaper, we propose a direct construction of 2-D Z-complementary array code set(ZCACS) by using multivariable function. For this purpose, we first proposed aconstruction of inter-group complementary (IGC) code set using multivariablefunction and use this construction to produce our desired 2-D ZCACS. The use ofmultivariable function enables us to set the size of the 2-D ZCACS to be $L_1\times L_2$, where $L_1= 2^m$, $L_2= 2 p_1^{m_1} p_2^{m_2} \dots p_k^{m_k}$, $m\geq 1$ and $m_\alpha \geq 2$ for all $\alpha=1,2, \dots, k$, which is animprovement over the traditional generalized Boolean function that producessequences of length of the form $2^m$.

Construction of Inter-Group Complementary Code Set and 2-D Z-Complementary Array Code Set Based on Multivariable Functions