A construction of a two-dimensional zero correlation zone array set based on generalized Boolean functions

In this paper, for the first time, we propose a direct construction of the two-dimensional (2D) zero correlation zone (ZCZ) array set based on a generalized Boolean function, which does not require any particular array as seed. The proposed construction generates $ 2^{\lambda+1} $ ZCZ array sets of dimension $ (2^n,2^{m+\lambda+2}) $ with ZCZ width $ ({2^n-1, 2^m}) $, where $ m,n \geq \lambda $ are positive integers. The proposed construction finds its application in bar codes, position detection, diffraction patterns for calibrating a laser beam, sound source arrays, phased array antennas, position detection arrays, spatial correlation and time-frequency coding.