F2上第三类向量深度的分布及序列{(E-1)^m(s)}m≥0的周期

On the third depth distribution and the period of sequence {(E-1)～m(s)}_(m≥0) over F_2

向量复杂程度的一个研究角度是向量的深度。将Etzion和Roth提出的向量深度归纳为3类向量深度,通过有限长序列的周期与第三类向量深度之间的关系,给出了F2上任意n维向量空间的第三类向量深度的分布,并且利用向量算子的矩阵描述,从序列{(E-1)m(s)}m≥0终归周期的角度,进一步考察了第三类向量深度为∞的向量的性质。

The complexity of a vector can be investigated in terms of three kinds of depths, which were introduced by Etzion and Roth. The third depth distribution of F2 was provided according to the relationship of period and the third depth of finite sequences. Then the ultimate period of sequence {（E-1）m（s）}^m≥0 was considered, when the third depth of the vector s is ∞.