On the linear complexities of two classes of quaternary sequences of even length with optimal autocorrelation
On the linear complexities of two classes of quaternary sequences of even length with optimal autocorrelation
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两类最优自相关偶数四元序列的线性复杂度
DOI：
10.3934/amc.2018031
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发表时间：
2018
影响因子：
0.9
通讯作者：
Chen Zhixiong
中科院分区：
文献类型：
--
作者：
Ke Pinhui;Jiang Yueqin;Chen Zhixiong
设 \begin{document}$q$\end{document} 为大于 4 的素数。本文确定两类具有最佳自相关的偶数长度四元序列在有限域 \begin{document}$\mathbb {F}_q$\end{document} 上的离散傅立叶变换系数。它们是从二元勒让德序列导出的周期为 \begin{document}$2p$\end{document} 的四元序列和从双素数序列对导出的周期为 \begin{document}$2p(p+2)$\end{document} 的四元序列。作为应用，确定了两个四元序列的有限域 \begin{document}$\mathbb {F}_q$\end{document} 上的线性复杂度。
Let \begin{document}$q$\end{document} be a prime greater than 4. In this paper, we determine the coefficients of the discrete Fourier transform over the finite field \begin{document}$\mathbb {F}_q$\end{document} of two classes of quaternary sequences of even length with optimal autocorrelation. They are quaternary sequence with period \begin{document}$2p$\end{document} derived from binary Legendre sequences and quaternary sequence with period \begin{document}$2p(p+2)$\end{document} derived from twin-prime sequences pair. As applications, the linear complexities over the finite field \begin{document}$\mathbb {F}_q$\end{document} of both of the quaternary sequences are determined.