一类可控序列线性复杂度的估计

本文运用指数集的概念，得到了任意有限域ＧＦ（ｑ）（ｑ＝ｐｍ）上Ｌ级ｍ－序列的多项式序列的线性复杂度，并导出了一类可控序列线性复杂度的上界，这个上界很可能是紧上界。当域特征ｐ＝２时，这类序列线性复杂度的上界为Ｌ＋１２［（Ｌ＋１）ｍ－１］，下界为［（Ｌ＋１）ｍ－１］。

Estimating the Complexity of a Class of Controllable Sequence

With the concept of exponent set introduced, the complexity of polynomial sequences of an m sequence of degree L over any finite field GF(q) (q=p m) is obtained, and an upper bound of the complexity of a class of controllable sequence is derived which appears to be the tight one. In the case of field characteristic p=2, this class of sequence has an upper bound L 12(L 1) m-1] and a lower bound (L 1) m-1] of complexity.