Abstract
<p style='text-indent:20px;'>Let <inline-formula><tex-math id="M1">\begin{document}$ p\equiv 1\pmod 3 $\end{document}</tex-math></inline-formula> be a prime. In this paper, we determine the 2-adic complexity of all non-trivial balanced cyclotomic binary sequences of order three with period <inline-formula><tex-math id="M2">\begin{document}$ 2p $\end{document}</tex-math></inline-formula> and the 2-adic complexity of several non-balanced cyclotomic binary sequences of order three with period <inline-formula><tex-math id="M3">\begin{document}$ 2p $\end{document}</tex-math></inline-formula>.</p>
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