来自函数域的大线性复杂度和错误线性复杂度的多序列
Multi-sequences with large linear and error linear complexity from function fields
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中文总结 AI 辅助
本文提出一种基于函数域构造周期多序列的通用框架，证明其具有大的线性复杂度和错误线性复杂度，并应用于极大函数域，获得多种新序列及准循环代数几何码。
中文摘要 AI 辅助
多序列的线性复杂度和错误线性复杂度是流密码中安全性的度量。在本文中，我们提出了一个通过函数域构造周期多序列的一般框架。我们证明了所构造的多序列同时具有大的线性复杂度和大的错误线性复杂度。我们将此构造多序列的框架应用于各种极大函数域，并获得了许多具有不同长度和维度的新多序列。作为副产品，我们采用这一思想，也产生了许多新的准循环代数几何码。
英文摘要
The linear complexity and the error linear complexity of multi-sequences are measures for security in stream ciphers. In this manuscript, we present a general framework for constructing periodic multi-sequences via function fields. We prove that the constructed multi-sequences possess both large linear complexity and large error linear complexity. We apply this framework of constructing multi-sequences to various maximal function fields and we obtain many new multi-sequences with various lengths and dimensions. As a byproduct, we adopt this idea and produce many new quasi-cyclic algebraic geometric codes as well.
发表机构
- University of Science and Technology of China（中国科学技术大学）
- National Key Laboratory of Science and Technology on Communications, University of Electronic Science and Technology of China（电子科技大学通信抗干扰理论国家级重点实验室）
- Shanghai Jiao Tong University（上海交通大学）
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