Two classes of optimal quaternary sequences have been constructed by applying the sign alternation transform and Gray mapping to Legendre sequence pair, twin-prime sequence pair and GMW sequence pair. In this paper, a new method for investigating the linear complexity over finite field is proposed, and the exact values of the linear complexity over finite field \({\mathbb {F}}_4\) and Galois ring \({\mathbb {Z}}_4\) of the quaternary sequences are determined. The results show that their linear complexity are quite good.

中文翻译：

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基于符号交替变换的两类四元序列的线性复杂度

将符号交替变换和格雷映射应用于Legendre序列对、双素数序列对和GMW序列对，构造了两类最优四元序列。本文提出了一种研究有限域线性复杂度的新方法，以及有限域线性复杂度\({\mathbb {F}}_4\)和 Galois ring \({\mathbb { Z}}_4\)的四元序列被确定。结果表明，它们的线性复杂度相当好。