\textit{M}序列由于具有良好的统计特性经常被应用在信息安全领域.这使得寻找$F_2$中\textit{M}序列反馈函数成为一项有意义的工作. 给出了由已知\textit{M}序列反馈多项式得出新的与已知函数同次数的\textit{M}序列反馈多项 式的新方法.主要工作如下: 1) 用图形简单的给出了并圈法 的逆过程所实现的操作过程. 2) 将并圈法的逆运算与并圈法先后应用在已有\textit{M}序列状态图交叉排列的两对前共轭顶点对上,得到了由已知\textit{M}序列反馈多项式生成新\textit{M}序列反馈多项式的算法.3) 证明了上述给出算法在二阶有限域$F_2$中的正确性.4) 用C 语言实现了算法.实验结果表明当移位寄存器的阶不是很大时算法是有效的.

M sequences are used in secure communication due to their good statistical properties. Hence, seeking new M sequence feedback polynomials in F2 becomes a meaning- ful work. In this paper, we put forward a new method for generating M sequence feedback polynomials in F2 from the given M sequence feedback polynomials with the same order. Our main work is as follows: Firstly, we present the main operation realized by the converse of
amalgamating-circles method using graphs. Secondly, we apply the converse of amalgamating- circles method and itself alternately on two pairs of front-conjugate and intersecting vertexes on the state graph of the known M-sequences, and thus give an algorithm for generating new M sequence feedback polynomials from the given M sequence feedback polynomials. Then we prove that the given algorithm is correct in F2. Finally, we implement the algorithm in C language. Experimental results indicate that the algorithm is efficient when the order n of the shift register is moderate.