反馈移位寄存器非奇异性研究

Criterion for the Nonsingularity of Feedback Shift Registers

本文给出q元有限域上的反馈移位寄存器非奇异性判定的充分必要条件,并利用Groebner基理论对定理给出的条件进行约化,给出了q=3,4,5时任意次反馈函数非奇异性的充要条件。

This paper presents the necessary and sufficient conditions for the nonsingularity of feedback shift registers on the q element finite field, and shows the necessary and sufficient conditions for the nonsingularity of feedback shift registers on q= 3,4,5 with the theory of the Groebner basis.