<p style='text-indent:20px;'>Aperodic (or called Golay)/Periodic complementary pairs (GCPs/ PCPs) are pairs of sequences whose aperiodic/periodic autocorrelation sums are zero everywhere, except at the zero shift. In this paper, we introduce GCPs/PCPs over the quaternion group <inline-formula><tex-math>\begin{document}$ Q_8 $\end{document}</tex-math></inline-formula>, which is a generalization of quaternary GCPs/PCPs. Some basic properties of autocorrelations of <inline-formula><tex-math>\begin{document}$ Q_8 $\end{document}</tex-math></inline-formula>-sequences are also obtained. We present three types of constructions for GCPs and PCPs over <inline-formula><tex-math>\begin{document}$ Q_8 $\end{document}</tex-math></inline-formula>. The main ideas of these constructions are to consider pairs of a <inline-formula><tex-math>\begin{document}$ Q_8 $\end{document}</tex-math></inline-formula>-sequence and its reverse, pairs of interleaving of sequence, or pairs of Kronecker product of sequences. By choosing suitable sequences in these constructions, we obtain new parameters for GCPs and PCPs, which have not been reported before.</p>

中文翻译：

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四元数上的非周期性/周期性互补序列对

<p style='text-indent:20px;'>非周期性（或称为 Golay）/周期性互补对 (GCP/PCP) 是非周期性/周期性自相关和除零偏移外处处为零的序列对。在本文中，我们介绍了四元组 <inline-formula><tex-math>\begin{document}$ Q_8 $\end{document}</tex-math></inline-formula> 上的 GCPs/PCPs，它是四元 GCP/PCP 的概括。还获得了<inline-formula><tex-math>\begin{document}$ Q_8 $\end{document}</tex-math></inline-formula>-sequences的自相关的一些基本性质。我们提出了三种类型的 GCP 和 PCP 在 <inline-formula><tex-math>\begin{document}$ Q_8 $\end{document}</tex-math></inline-formula> 上的构造。这些结构的主要思想是考虑成对的 <inline-formula><tex-math>\begin{document}$ Q_8 $\end{document}</tex-math></inline-formula>-sequence 和其相反，序列的交错对，或序列的 Kronecker 乘积对。通过在这些结构中选择合适的序列，我们获得了GCPs和PCPs的新参数，这是以前没有报道过的。</p>