Binary periodic sequences with good autocorrelation property have many applications in many aspects of communication. In past decades many series of such binary sequences have been constructed. In the application of cryptography, such binary sequences are required to have larger linear complexity. Tang and Ding \cite{X. Tang} presented a method to construct a series of binary sequences with period 4$n$ having optimal autocorrelation. Such sequences are interleaved by two arbitrary binary sequences with period $n\equiv 3\pmod 4$ and ideal autocorrelation. In this paper we present a general formula on the linear complexity of such interleaved sequences. Particularly, we show that the linear complexity of such sequences with period 4$n$ is not bigger than $2n+2$. Interleaving by several types of known binary sequences with ideal autocorrelation ($m$-sequences, Legendre, twin-prime and Hall's sequences), we present many series of such sequences having the maximum value $2n+2$ of linear complexity which gives an answer of a problem raised by N. Li and X. Tang \cite{N. Li}. Finally, in the conclusion section we show that it can be seen easily that the 2-adic complexity of all such interleaved sequences reaches the maximum value $\log_{2}(2^{4n}-1)$.
翻译:具有良好自动关系属性的二进制周期序列在许多通信方面有许多应用。 在过去的几十年里, 许多这样的二进制序列已经构建。 在加密应用中, 这种二进制序列需要具有更大的线性复杂性。 唐和 Ding\ cite{X. 唐 和 Ding\ cite{X. Tang} 提出了一个方法来构建一系列的二进制序列, 4 年周期为 $n美元, 具有最佳的自动关系。 这些序列由两个任意的二进制序列互连在一起, 期间为 $\ equiv 3\ pmod 4$ 和理想的自动关系。 在本文中, 我们给出了这些序列的通用公式, 此类序列的线性复杂性为 线性公式为 4 n+2 美元 。 特别是, 我们展示了这些序列的线性序列的线性复杂性线性复杂性不大于 $ 2 $ 2 。 里尔 解说, 最终可以解析 X 。