Construction of Inter-Group Complementary Code Set and 2-D Z-Complementary Array Code Set Based on Multivariable Functions
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The need of two dimensional (2-D) arrays with good 2-D correlation properties have been found of great interest in research because of the rapid development of the modern technologies in the field of wireless communications. 2-D arrays have found various applications wireless communication technologies such as ultra-wide band (UWB), 2-D synchronization, phased array antenna etc. In this paper, we propose a direct construction of 2-D Z-complementary array code set (ZCACS) by using multivariable function. For this purpose, we first proposed a construction of inter-group complementary (IGC) code set using multivariable function and use this construction to produce our desired 2-D ZCACS. The use of multivariable function enables us to set the size of the 2-D ZCACS to be L_1 × L_2, where L_1= 2^m, L_2= 2 p_1^m_1 p_2^m_2… p_k^m_k, m ≥ 1 and m_α≥ 2 for all α=1,2, …, k, which is an improvement over the traditional generalized Boolean function that produces sequences of length of the form 2^m.
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