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| 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 |
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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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Received: 13 April 2009
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Corresponding Authors:
Tu Yi-feng
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2010, Vol. 32 
