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.
采用反馈移位寄存器与逻辑门设计了三个典型的编码器电路：基于SRAA电路的串行准循环LDPC码编码器；
Three encoder circuit are designed respectively with feed shift-registers and logic gates: SRAA-based serial QC-LDPC encoder;
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