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.
The Fourier polynomial fitting is compared with the Chebysher polynomial fitting in the division of cyclic time interval and fitting accuracy as well as convergence of function.
将本方法在周期时段划分、拟合精度、函数收敛方面与契比雪夫多项式拟合法进行了对比。
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In the case of(Char(F_q), |G|)=1, we provide a method that writing down directly all the primitive idempotents of related polynomial ring, and hence that of all the minimum cyclic codes.