几类伪随机序列的线性复杂度和2-adic复杂度及其稳定性分析

伪随机序列已被广泛应用于密码、通信和雷达等诸多领域，序列的线性复杂度和2-adic复杂度是衡量其在实际应用中安全性的重要指标。本项目拟综合运用有限域、有限环、数论以及组合数学等理论工具，设计几类新型伪随机序列，主要包括基于分圆类所构造的序列、基于交织结构所生成的序列、基于比特分位而生成的序列以及由这些构造方式进行交叉融合而得到的新型序列，并分析这些序列的线性复杂度和2-adic复杂度性质及其稳定特性，以便为相关工程应用提供相应的理论支撑。

Pseudo-random sequences are widely used in many fields, such as cryptography, communication and radar. The linear complexity and the 2-adic complexity of a sequence are two important indexes to measure its security in practical applications. Several new classes of pseudo-random sequences, which include new sequences based on cyclotomic classes, interleaving technique, bit-component and new sequences generated from cross-fusion of these constructions, are to be designed in this project. The linear complexities and the 2-adic complexities and their stabilities of these sequences will be analyzed using some theoretic tools, such as finite fields, finite rings, number theory and combinatorics. Our results will provide corresponding theoretic support for related engineering applications.