最佳三元序列设计

Perfect Ternary Sequences Design

介绍最佳三元序列成立的必要条件。最佳序列的置换群,存在一个乘法子群,在它的作用下得到的序列为原序列的循环移位。最佳序列及其循环移位构成序列的一个等价类,且在每个等价类中,至少存在一个序列,在该乘法群的作用下序列不变,即在等价类中乘法群存在不动点。利用群的不动点理论和最佳序列成立的必要条件构造最佳序列,给出了相同参数序列的个数及构造序列所遵循的原则,并举例说明。

Perfect ternary sequence （PTS） design is introduced. First the necessary conditions of PTS are discussed. There is a muhiplicativc group among the permutation groups, the sequence obtained under the action of it is cyclic shift of related PTS, and the perfect sequence and its cyclic shifts compose an equivalence class.Among any equivalence class,there is at least a sequence,which is the fixed point of the multiplicative group. The fixed point theory and necessary conditions of the perfect sequence are used, the constructive method is proposed, and the number of equivalence classes and the principle for constructing sequence are given, and illustrated with some examples.