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产生同一 m 序列,可以有不同结构的发生器,它们对应不同的变换矩阵。本文从代数编码理论出发,讨论了 m 序列发生器变换矩阵的基本性质。说明变换矩阵不仅表征了 m 序列的全部性质,而且决定了发生器状态矢量各分量的关系和它经历的特定流程。从某个 m 序列发生器变换矩阵出发,进行方幂运算、非退化线性变换,可以得到同样长度 m 序列的任一种可能的变换矩阵。以周期为15和31的变换矩阵为例,解释变换矩阵的特性。最后以变换矩阵为工具,给出两个实用 m 序列发生器的逻辑设计。
Produce the same m sequence, there can be different structure of the generator, they correspond to different transformation matrix. Based on algebraic coding theory, this paper discusses the basic properties of the m-sequence generator transformation matrix. It shows that the transformation matrix not only characterizes all the properties of the m-sequence, but also determines the relationship between the components of the generator state vector and the specific processes it undergoes. Starting from the transformation matrix of a m-sequence generator, a power operation and a non-degenerate linear transformation are performed to obtain any possible transformation matrix of m sequences with the same length. Taking the transformation matrices of period 15 and 31 as an example, the characteristics of the transformation matrices are explained. Finally, using the transformation matrix as a tool, we give the logic design of two practical m sequence generators.