特征向量在LFSR序列分析中的应用

The Use of Eigenvector in Analyzing the Output Sequences of LFSR

利用线性反馈移位寄存器 ( L FSR)的生成多项式的矩阵表示 ,通过对该矩阵的特征向量分析 ,给出了线性反馈移位寄存器输出结果的明确表达式 ,其中的系数完全依赖于初始输入值及其极小多项式的互反多项式的根。所得结果对 L FSR的性质作了更进一步的揭示 。

Through the use of matrix representation of the minimum generation polynomial of a linear feedback shift register and the analysis of eingenvector of the matrix,a more accurate expression of the output sequence of the linear feedback shift register is presented,in which the coefficient of the expression is completely determined by the initial input values of the sequence and the roots of the reciprocal polynomial of the mimimum generation polynomial. The result presents a further revelation of the nature of a linear feedback shift register and is much more definite than the known conclusions.