Analysis and Construction of Golay Pair Based on Generating Function
Tu Yi-feng①,Shinya Matsufuji②,Fan Ping-zhi①,Li Xu-dong①
①Provincial Key Lab of Information Coding & Transmission, Institute of Mobile Communications, Southwest Jiaotong University, Chengdu, 610031, China; ②Graduate School of Science and Engineering, Yamaguchi University, 2-16-1 Tokiwadai, Ube, Yamaguchi, 755-8611, Japan
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.
涂宜锋,松藤信哉,范平志,李旭东. 基于生成函数的格雷对分析与构造[J]. 电子与信息学报, 2010, 32(2): 335-339 .
Tu Yi-feng①,Shinya Matsufuji②,Fan Ping-zhi①,Li Xu-dong①. Analysis and Construction of Golay Pair Based on Generating Function. , 2010, 32(2): 335-339 .
2010, Vol. 32 
