基于生成函数的格雷对分析与构造

涂宜锋; 松藤信哉; 范平志; 李旭东

doi:10.3724/SP.J.1146.2009.00533

基于生成函数的格雷对分析与构造

doi: 10.3724/SP.J.1146.2009.00533

涂宜锋^①,,
松藤信哉^②,
范平志^①,
李旭东^①

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出版历程
- 收稿日期: 2009-04-13
- 修回日期: 2009-09-16
- 刊出日期: 2010-02-19

Analysis and Construction of Golay Pair Based on Generating Function

摘要

摘要: 该文由传统的格雷对构造方法交织和级联出发，提出了一种新的称之为生成函数的格雷对构造方法，该方法适用于长度为2n 的格雷对。文中分析了格雷对生成函数和希尔维斯特Hadamard矩阵之间的关系，这不仅有助于计算给定长度的格雷对的数量，而且有助于将Hadamard分解应用于格雷对的生成中。采用生成函数，可以很方便地产生一系列的格雷对应用于多目标的环境。格雷对生成函数由二进制向量，与和或逻辑运算组成，极大地方便了序列生成器的硬件实现。
- 格雷对; 自相关函数; 互相关函数; 生成函数
Abstract: In this paper, an approach called generating function is proposed to construct Golay pair of length 2n and its mate based on conventional interleaving and concatenation method. Relationship between generating function of Golay pair and Sylvester Hadamard matrix is also investigated, which not only helps to calculate the total number of Golay pair of specific length, but also helps to apply Hadamard factorization to Golay pair generation. Based on generating function, lots of Golay pair can be produced conveniently for multi-target applications. Generating functions are expressed by binary vector, XOR and AND operations, which greatly facilitates the physical implementation of sequence generation.

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参考文献(1)

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