二元互补序列的特征序列

本文引入互补序列的特征序列的概念,定义每个互补序列包含两种特征序列,分别记为1-特征序列和2-特征序列.特征序列对研究互补序列的特性具有重要意义.经分析发现当序列长度时N≥4,可以根据特征序列来判断互补序列等价类空间大小是32还是64,这对实际应用中互补序列的选取具有一定意义;本文对互补序列的各种构造方法进行了分析,发现通过每种构造方法构造出的互补序列其特征序列均具有某种特性,本文论证得出可以通过特征序列来判断互补序列是否是可构造的以及可以由哪种构造方法构造,并通过特征序列证实了长度为20的互补序列的核的存在性.

The Feature Sequence of Complementary Sequences

The feature sequences of complementary sequences are introduced in this paper.Every complementary sequence has two kinds of feature sequences.Each equivalence class has 64 or 32 complementary sequences.When the length of complementary is not less then 4,it can determine which equivalence class has 64 or 32 by the feature sequences of this class.When the complementary sequences can be constructed,it is called constructible complementary sequence.Now there are 5 constructive methods have been found,through which all of the complementary sequences whose length is 2r10s26t can be constructed.It can determine which equivalence class is constructible or not by the feature sequence.