论文标题
互补序列（或数组）集和完整互补代码的新结构
New Construction of Complementary Sequence (or Array) Sets and Complete Complementary Codes
论文作者
论文摘要
构建$ q $ - y-ary互补序列集（CSS）和尺寸$ n $的完整互补代码（CCC）的新方法是通过使用所需的para-nitiral（pu）矩阵提出的。引入了种子PU矩阵的概念，并采用了如何计算从种子PU矩阵中构造的CSS和CCC中的函数的明确形式的系统方法。这些函数的一般形式仅取决于函数的基础，从$ \ z_n $到$ \ z_q $以及在Butson-Type Hadamard（BH）矩阵的等效类中的代表。尤其是，从我们的一般形式中实现戈莱对与标准的戈莱对完全一致。首先报道了$ 3 $的三元互补序列的实现。为了实现第四大小4的第四纪互补序列，此处得出的几乎所有序列从未报道过。还研究了普遍的种子PU矩阵和所需PU矩阵的递归结构，并相应地给出了大量CSS和CCC的新构建体。从本文的角度来看，文献中具有明确GBF形式的CSS和CCC的所有已知结果（非标准的Golay对除外）都是由命令2的Walsh矩阵构建的。这表明，与较高级数的BH矩阵相关的提议方法将产生大量的新cccs和CCC的序列，该序列会增加数量的数量，该序列增加了数量的数量，这些数字会增加数量的数量。 比率。
A new method to construct $q$-ary complementary sequence sets (CSSs) and complete complementary codes (CCCs) of size $N$ is proposed by using desired para-unitary (PU) matrices. The concept of seed PU matrices is introduced and a systematic approach on how to compute the explicit forms of the functions in constructed CSSs and CCCs from the seed PU matrices is given. A general form of these functions only depends on a basis of the functions from $\Z_N$ to $\Z_q$ and representatives in the equivalent class of Butson-type Hadamard (BH) matrices. Especially, the realization of Golay pairs from the our general form exactly coincides with the standard Golay pairs. The realization of ternary complementary sequences of size $3$ is first reported here. For the realization of the quaternary complementary sequences of size 4, almost all the sequences derived here are never reported before. Generalized seed PU matrices and the recursive constructions of the desired PU matrices are also studied, and a large number of new constructions of CSSs and CCCs are given accordingly. From the perspective of this paper, all the known results of CSSs and CCCs with explicit GBF form in the literature (except non-standard Golay pairs) are constructed from the Walsh matrices of order 2. This suggests that the proposed method with the BH matrices of higher orders will yield a large number of new CSSs and CCCs with the exponentially increasing number of the sequences of low peak-to-mean envelope power ratio.
