  This paper is devoted to sequences and focuses on designing new
two-dimensional (2-D) Z-complementary array pairs (ZCAPs) by exploring two
promising approaches. A ZCAP is a pair of 2-D arrays, whose 2-D autocorrelation
sum gives zero value at all time shifts in a zone around the $(0,0)$ time
shift, except the $(0,0)$ time shift. The first approach investigated in this
paper uses a one-dimensional (1-D) Z-complementary pair (ZCP), which is an
extension of the 1-D Golay complementary pair (GCP) where the autocorrelations
of constituent sequences are complementary within a zero correlation zone
(ZCZ). The second approach involves directly generalized Boolean functions
(which are important components with many applications, particularly in
(symmetric) cryptography). Along with this paper, new construction of 2-D ZCAPs
is proposed based on 1-D ZCP, and direct construction of 2-D ZCAPs is also
offered directly by 2-D generalized Boolean functions. Compared to existing
constructions based on generalized Boolean functions, our proposed construction
covers all of them. ZCZ sequences are a class of spreading sequences having
ideal auto-correlation and cross-correlation in a zone around the origin. In
recent years, they have been extensively studied due to their crucial
applications, particularly in quasi-synchronous code division multiple access
systems. Our proposed 2-D ZCAPs based on 2-D generalized Boolean functions have
larger 2-D $\mathrm{ZCZ}_{\mathrm{ratio}}=\frac{6}{7}$. Compared to the
construction based on ZCPs, our proposed 2-D ZCAPs also have the largest 2-D
$\mathrm{ZCZ}_{\mathrm{ratio}}$.
