具有大线性复杂度的最优部分汉明相关跳频序列集的构造研究

Owing to the advantages of anti-interference, low probability of interception and multiple address netting of frequency-hopping(FH) sequences，they are widely used in modern communication systems such as radar, sonar, bluetooth, 4G mobile and military. The construction of FH sequence set has became the emerging topic of modern communication systems in recent years..This project mainly studies the construction of optimal partial Hamming correlation FH sequence set with large linear complexity. Firstly, using the theory and method of algebra, finite field, number theory, combinatorics and coding, we construct some optimal partial Hamming correlation FH sequence sets with respect to the known APH low bound or improve the known APH low bound, then construct some optimal FH sequence sets with flexible parameters; Secondly, we discuss the linear complexity of the above FH sequence sets. We obtain the desired FH sequence sets if their linear complexity is large enough; Otherwise, using the generalised Bent function or permutation polynomials (power permutation/δ(x) permutation), we can obtain some FH sequence sets with optimal partial Hamming correlation and large linear complexity based on the above FH sequence sets.

跳频序列具有抗干扰、低截获和多址组网等优点，在现代通讯如雷达、声呐、蓝牙、4G移动通讯及军事通讯中具有广泛的应用。近年来已成为无线网络通讯领域研究的热点。.本项目主要研究具有大线性复杂度的最优部分汉明相关跳频序列集的构造。首先，就部分汉明相关（PHC）而言，利用已知的跳频序列集部分汉明相关性的下界或者运用代数、有限域、数论、组合以及编码理论对已知下界进行改进，得出跳频序列集部分汉明相关性的更紧的下界，进而构造出几类最优跳频序列集，使得该跳频序列集具有更加灵活的参数；其次，计算该跳频序列集的线性复杂度。如果其线性复杂度足够大，那么该跳频序列集符合要求。否则，在上面得到的小线性复杂度的跳频序列集的基础上，运用广义Bent函数或置换多项式（幂置换/δ(x)置换）思想来构造大线性复杂度的跳频序列集，并保持原跳频序列集的最优部分汉明相关性不变。