中文摘要：

线性变换移位寄存器由Tsaban和Vishne提出,是一个面向字的移位寄存器,每次输出一个字节。研究了由TSR所生成的序列的基本性质,并且给出了一个新的准则来判定一个线性变换移位寄存器系统的特征多项式是否不可约。利用这个准则,不需要在扩域上做运算来判定一个线性变换移位寄存器系统的特征多项式是否不可约。

英文摘要：

Linear transformation shift registers（TSR） were introduced by Tsaban and Vishne, which was a word-oriented shift register output a word per step. Some basic properties of sequences generated by the TSR were presented, and a new criterion for deciding if the characteristic polynomial of a TSR system is irreducible was given. This criterion avoids operations in extension fields.