本文给出有限域上多项式周期存在的构造性证明，利用它可求出多项式的周期。
This paper gives a constructive proof of existence of period of polynomials infinite field. Using it we can also find the period of polynomials.
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.
本文给出了有限域上单变元多项式分解的一种概率算法。
A probabilistic algorithm for factoring univariate polynomials over finite fields is presented.
与在向量空间上构造的方法比，有限域上置换多项式的代数次数等性质更容易研究。
Compared to the construction over vector space, it is easier to study the properties of permutation polynomials, like algebraic degree.
对计算有限域上切比雪夫多项式的特征多项式算法进行改进以提高算法的执行速度。
A Characteristic polynomial algorithm for computation of Chebyshev polynomial over finite field is modified to achieve faster execution speed.
因此，有限域上的置换多项式一直是一个重要的研究课题，关于这一课题的研究至少有140年的历史。
Hence the research on permutation polynomials has been an important subject for at least 140 years, especially from 70s of the last century for the necessary of the study of cryptography.
因此，有限域上的置换多项式一直是一个重要的研究课题，关于这一课题的研究至少有140年的历史。
Hence the research on permutation polynomials has been an important subject for at least 140 years, especially from 70s of the last century for the necessary of the study of cryptography.
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