Jennings复合序列的一些补注

Some Annotations about the Multipled Jennings Sequences

引入了一组向量,用真值描述的方法对Jennings复合序列的定义进行了新的推导,并对该序列的有关周期、线性复杂度的定理的证明作了简化和补充.为了度量序列的稳定性,引入了重量复杂度WCk(u∞),给出了它的1-重量复杂度和2-重量复杂度下限;当1=k<m时,下限为(2m-1)(2n-1)-n(m+1);当2 k<m时,下限为(2m-1)(2n-1)-n∑ki=0Cmi;当k=m时,下限为(2m-1)(2n-1)-n(2m-1).分析了该序列线性复杂度的稳定性.

The paper presents a series of vectors, discusses the definitions about the muhipled Jennings sequences by giving the values to the vectors. Some reductions and complementaries on the period and the linear complexity of the proofs of the theory are also given. In order to measure the stability of the sequence, this paper introduces the weighty complexity WCk （ u^∞ ） and gets the lower limit when k is one and two, which is （2^m-1）（2^n-1）-n（m＋1） when 1 =k〈m;（2^m-1）（2^n-1） -∑i=0^kCm^i when2≤k〈m;（2^m-1）（2^n-1） -n （2^m - 1 ） when k = m. The case is the same when k is two. The stability of the linear complexity of the sequences is analysised.