本文给出了有限域上多项式的友矩阵的某些性质，及其在计算线性移位寄存器序列的周期和循环码的最小长度的应用。

This paper gives some properties of companion matrix of polynomial over finite field with its application for evaluating period of linear shift register sequence and minimal length of cyclic code.

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最后，”一丝不苟”VI 使用大量移位寄存器在一个循环内反复传递数据，在多个并行循环间使用队列传递数据。

Finally, Meticulous VI makes extensive use of shift registers for passing data between loop iterations, and queues for passing data between parallel loops.

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接着，针对生成矩阵的准循环特性，提出了一种新的基于反馈移位寄存器的编码电路，并用FPGA进行了实现。

Next, according to the characteristics of quasi-cyclic matrix, a new encoding circuit using feedback shift registers is proposed and implemented by FPGA.

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