Determination of the Autocorrelation Distribution and 2-Adic Complexity of Generalized Cyclotomic Binary Sequences of Order 2 with Period pq

Xiaoyan Jing; Shiyuan Qiang; Minghui Yang; Keqin Feng

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arXiv · 2105.10947

Determination of the Autocorrelation Distribution and 2-Adic Complexity of Generalized Cyclotomic Binary Sequences of Order 2 with Period pq

Xiaoyan Jing·Shiyuan Qiang·Minghui Yang·Keqin Feng

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Abstract

The generalized cyclotomic binary sequences $S=S(a, b, c)$ with period $n=pq$ have good autocorrelation property where $(a, b, c)\in \{0, 1\}^3$ and $p, q$ are distinct odd primes. For some cases, the sequences $S$ have ideal or optimal autocorrelation. In this paper we determine the autocorrelation distribution and 2-adic complexity of the sequences $S=S(a, b, c)$ for all $(a, b, c)\in \{0, 1\}^3$ in a unified way by using group ring language and a version of quadratic Gauss sums valued in group ring $R=\mathbb{Z}[\Gamma]$ where $\Gamma$ is a cyclic group of order $n$.

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Xiaoyan Jing, Shiyuan Qiang, Minghui Yang, Keqin Feng. 2021-05-23. Determination of the Autocorrelation Distribution and 2-Adic Complexity of Generalized Cyclotomic Binary Sequences of Order 2 with Period pq. https://arxiv.org/abs/2105.10947

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