具有交织结构和最佳自相关幅度的Yu-Gong序列的2-adic复杂度
The 2-adic complexity of Yu-Gong sequences with interleaved structure and optimal autocorrelation magnitude
摘要：
2008年，Yu和Gong基于$m$ -序列、周期为$4$的最佳序列$(0,1,1,1)$和交织技术，提出了一类具有最佳自相关幅度的周期为$N=4(2^k-1)(2^k+1)$的二元序列.本文研究了这类序列的2-adic复杂度。结果表明，它们都大于$N-2\lceil\mathrm{log}_2N\rceil+4 $（$N-2\lceil\mathrm{log}_2N\rceil+4 $远大于$N$），如果选择合适的参数，这类交织序列的2-adic复杂度大到足以抵抗有理近似算法。
英文摘要：
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.
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