  The sequence pairs of length $2^{m}$ projected from complementary array pairs
of Type-II of size $\mathbf{2}^{(m)}$ and mixed Type-II/III and of size
$\mathbf{2}^{(m-1)}\times2$ are complementary sequence pairs Type-II and
Type-III respectively. An exhaustive search for binary Type-II and Type-III
complementary sequence pairs of small lengths $2^{m}$ ($m=1,2,3,4$) shows that
they are all projected from the aforementioned complementary array pairs, whose
algebraic normal forms satisfy specified expressions. It's natural to ask
whether the conclusion holds for all $m$. In this paper, we proved that these
expressions of algebraic normal forms determine all the binary complementary
array pairs of Type-II of size $\mathbf{2}^{(m)}$ and mixed Type-II/III of size
$\mathbf{2}^{(m-1)}\times2$ respectively.
