%0 Journal Article
%T <i>Z</i><sub>4</sub>上一类四元广义分圆序列的线性复杂度<br>Linear Complexity of a Class of Quaternary Sequence Generated by Generalized Cyclotomic Class over <i>Z</i><sub>4</sub>
%A 邹蒙
%A 赵璐
%J Pure Mathematics
%P 33-38
%@ 2160-7605
%D 2025
%I Hans Publishing
%R 10.12677/pm.2025.152043
%X 序列的线性复杂度与序列的安全性息息相关。本文利用Galois理论&#65292;研究了一类在有限域<i>F</i><sub>4</sub>上具有较高线性复杂度的四元序列&#65292;得到了其在Galois环<i>Z</i><sub>4</sub>上的线性复杂度的确切值。结果显示&#65292;这类序列在Galois环<i>Z</i><sub>4</sub>上也具有较高的线性复杂度&#65292;可以较好地抵抗Reeds-Sloane算法的攻击。<br>The linear complexity of a sequence is closely related to its cryptographic security. In this paper, we employ Galois theory to investigate a class of quaternary sequence over the finite field <i>F</i><sub>4</sub> with high linear complexity, and determine the exact value of its linear complexity over the Galois ring <i>Z</i><sub>4</sub>. The results demonstrate that such sequence maintain relatively high linear complexity in the Galois ring <i>Z</i><sub>4</sub>, thereby exhibiting strong resistance against attacks by the Reeds-Sloane algorithm.
%K 四元序列&#65292
%K 线性复杂度&#65292
%K 分圆序列&#65292
%K Galois环<br>Quaternary Sequence
%K Linear Complexity
%K Cyclotomic Sequence
%K Galois Ring
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=107426