基于母函数的非线性反馈函数及其子序列研究

 针对非线性最大长度移位寄存器反馈函数难以构造问题,本文提出了一种基于母函数构造非线性最大长度移位寄存器反馈函数方法.首先,我们阐述了母函数模3分类法,证明了各类母函数新的特征状态集,提取了母函数的特征式;其次,根据特征式对母函数的筛分特性合成了非线性m子序列移位寄存器反馈函数;最后,分析了该移位寄存器生成的伪随机序列,对其自相关值和线性复杂度进行了大量搜索.结果一致表明该序列不仅具有良好的周期特性、平衡特性、游程特性,还具有尖锐的自相关特性和理想的线性复杂度.

Study of the Non-Linear Feedback Functions and a Class Subsequence Based on the Root-Functions

To solve the problem of constructing feedback functions of non-linear maximal length shift registers (NMLSR),the method to construct the feedback functions for NMLSR was proposed based on root function.First of all,we expatiated the classification method of the root functions modulo 3,proveded the characteristic state sets of the root functions and extracted the eigenfunctions of the root functions.Secondly,we synthesized the feedback function for the nonlinear m subsequence shift register according to the filter of the eigenfunctions on the root functions.Finally,we conducted a great number of calculations and analyses for new type sequences generated from the nonlinear m subsequence shift registers.The results show unanimously that the nonlinear m subsequences dose not only possess better period property,balance property and run-path property,but also the sharp autocorrelation property and the ideal linear complexity.