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arXiv · 2001.07393

The 2-adic complexity of Yu-Gong sequences with interleaved structure and optimal autocorrelation magnitude

Yuhua Sun·Tongjiang Yan·Qiuyan Wang
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Abstract

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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Yuhua Sun, Tongjiang Yan, Qiuyan Wang. 2020-01-21. The 2-adic complexity of Yu-Gong sequences with interleaved structure and optimal autocorrelation magnitude. https://arxiv.org/abs/2001.07393

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