Tang and Ding \cite{X. Tang} present a series of quaternary sequences $w(a, b)$ interleaved by two binary sequences $a$ and $b$ with ideal autocorrelation and show that such interleaved quaternary sequences have optimal autocorrelation. In this paper we consider the 4-adic complexity $FC_{w}(4)$ of such quaternary sequence $w=w(a, b)$. We present a general formula on $FC_{w}(4)$, $w=w(a, b)$. As a direct consequence, we get a general lower bound $FC_{w}(4)\geq\log_{4}(4^{n}-1)$ where $2n$ is the period of the sequence $w$. By taking $a$ and $b$ to be several types of known binary sequences with ideal autocorrelation ($m$-sequences, twin-prime, Legendre, Hall sequences and their complement, shift or sample sequences), we compute the exact values of $FC_{w}(4)$, $w=w(a, b)$. The results show that in most cases $FC_{w}(4)$ reaches or nearly reaches the maximum value $\log_{4}(4^{2n}-1)$.
翻译:唐氏 和 Ding 和 唐氏 和 唐氏 和 Ding 提出一系列四边序列 $w (a), b) 美元 。 作为直接结果,我们得到了一个一般的较低约束 $FC\w}(4)\ geq\log}(4 ⁇ n}-1美元,其中2美元是该序列的时期 $w。我们考虑四边序列的4美元复杂度 $FC\w}(4)(4) 美元 和 $b 美元是几种已知的二进制序列,具有理想的自动关系 美元(m) - 后果, 双金币, 格伦斯, 霍尔序列及其补充、 变化或抽样序列。作为直接后果,我们得到了一个一般较低约束的 $FC\w}(4)\ geq\log*4} (4} (4}-1美元) 美元, 美元是该序列中最接近的 美元 。