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arXiv · 2003.10939

A quaternion-based approach to construct quaternary periodic complementary pairs

Nitin Jonathan Myers·Robert W. Heath Jr
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Abstract

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.

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Nitin Jonathan Myers, Robert W. Heath Jr. 2020-03-24. A quaternion-based approach to construct quaternary periodic complementary pairs. https://arxiv.org/abs/2003.10939

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