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 lengthof cyclic code.
It was found that the code length distribution was closely correlated with the shift symmetry properties of synchronized coding and was characterized by sequencing and non-integral power of 2.
研究发现：其码长分布与同步字的移位对称数密切相关，具有连续和非2的整数次幂等特点；
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Restoration of the fibular length was important to prevent talar shift and tilt.