In 2008, a class of binary sequences of period $N=4(2^k-1)(2^k+1)$ with optimal autocorrelation magnitude has been presented by Yu and Gong based on an $m$-sequence, the perfect sequence $(0,1,1,1)$ of period $4$ and interleaving technique. In this paper, we study the 2-adic complexities of these sequences. Our results show that they are larger than $N-2\lceil\mathrm{log}_2N\rceil+4 $ (which is far larger than $N/2$) and could attain the maximum value $N$ if suitable parameters are chosen, i.e., the 2-adic complexity of this class of interleaved sequences is large enough to resist the Rational Approximation Algorithm.

中文翻译：

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具有交错结构和最佳自相关幅度的愚公序列的2-adic复杂度

2008年，Yu和Gong基于$m$-序列提出了一类周期$N=4(2^k-1)(2^k+1)$的具有最佳自相关幅度的二进制序列，完美序列 $(0,1,1,1)$ 的周期 $4$ 和交织技术。在本文中，我们研究了这些序列的 2-adic 复杂性。我们的结果表明它们大于 $N-2\lceil\mathrm{log}_2N\rceil+4 $（远大于 $N/2$）并且如果合适的参数可以达到最大值 $N$选择，即此类交错序列的 2-adic 复杂度足够大以抵抗有理逼近算法。