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arXiv · 1512.03871

On the Linear Complexity of Generalized Cyclotomic Quaternary Sequences with Length $2pq$

Minglong Qi·Shengwu Xiong·Jingling Yuan·Wenbi Rao·Luo Zhong
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Abstract

In this paper, the linear complexity over $\mathbf{GF}(r)$ of generalized cyclotomic quaternary sequences with period $2pq$ is determined, where $ r $ is an odd prime such that $r \ge 5$ and $r\notin \lbrace p,q\rbrace$. The minimal value of the linear complexity is equal to $\tfrac{5pq+p+q+1}{4}$ which is greater than the half of the period $2pq$. According to the Berlekamp-Massey algorithm, these sequences are viewed as enough good for the use in cryptography. We show also that if the character of the extension field $\mathbf{GF}(r^{m})$, $r$, is chosen so that $\bigl(\tfrac{r}{p}\bigr) = \bigl(\tfrac{r}{q}\bigr) = -1$, $r\nmid 3pq-1$, and $r\nmid 2pq-4$, then the linear complexity can reach the maximal value equal to the length of the sequences.

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Minglong Qi, Shengwu Xiong, Jingling Yuan, Wenbi Rao, Luo Zhong. 2016-02-26. On the Linear Complexity of Generalized Cyclotomic Quaternary Sequences with Length $2pq$. https://doi.org/10.1587/transfun.e98.a.1569

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