  Two arrays form a periodic complementary pair if the sum of their periodic
autocorrelations is a delta function. Finding such pairs, however, is
challenging for large arrays whose entries are constrained to a small alphabet.
One such alphabet is the quaternary set which contains the complex fourth roots
of unity. In this paper, we propose a technique to construct periodic
complementary pairs defined over the quaternary set using perfect quaternion
arrays. We show how new pairs of quaternary sequences, matrices, and
four-dimensional arrays that satisfy a periodic complementary property can be
constructed with our method.
