Aperiodic/periodic complementary sequence pairs over quaternions

Aperodic (or called Golay)/Periodic complementary pairs (GCPs/ PCPs) are of sequences whose aperiodic/periodic autocorrelation sums zero everywhere, except at the shift. In this paper, we introduce GCPs/PCPs over quaternion group \begin{document}$ Q_8 $\end{document}, which is a generalization quaternary GCPs/PCPs. Some basic properties autocorrelations id="M2">\begin{document}$ $\end{document}-sequences also obtained. We present three types constructions for GCPs and PCPs id="M3">\begin{document}$ $\end{document}. The main ideas these to consider id="M4">\begin{document}$ $\end{document}-sequence its reverse, interleaving sequence, or Kronecker product sequences. By choosing suitable in constructions, obtain new parameters PCPs, have not been reported before.