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.
对准循环Q矩阵和完全循环差集进行了研究，在此基础上提出了一种LDPC码码族的代数构造方法。
This paper presents an algebra method for constructing LDPC code based on Vandermonde matrix, which includes quasi-cyclic Q matrix and the perfect cyclic difference sets.
最后，在分块反对称反循环矩阵性质的基础上，给出了其特征值和特征多项式以及相似对角阵。
Finally, based on these characteristics, the eigenvalues and eigenvalues polynomials and its diagonal matrix were given.
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