在对d-FCSR结构进行分析的基础上,得出了连接数为q的d-FCSR的记忆范围为[0,w(q)],并且得出了d-FCSR记忆序列的周期与输出序列周期相同且记忆序列周期互补的性质。应用上述周期性质,得到一个有关代数整数环上周期因子分圆数不整除q的结论。
In this paper, the d-FCSR architecture is analyzed. It is showed that the memory range of d-FCSR with connection algebraic integer q is [ 0, w (q) ]. Additionally, the memory sequence is also studied. It is showed that the memory sequence has the period complementrity property and the memory sequence period is the same with the output sequence. As one consequence of this, a conclusion that the cyclotomic numbers of period factor do not divide the algebraic interger q is given.