二进制序列的重只定理和Hamming距离定理
WEIGHT THEOREM AND HAMMING DISTANCE THEOREMS OF BINARY SEQUENCES
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摘要: 本文系统地研究了二进制序列的重量与互相关函数旁瓣之和的关系,Hamming距离与游程数之间的关系,证明了普适的重量定理和Hamming距离定理,在此基础上,进一步研究了标准正交变换,正交码、互补码在Tseng分解过程中的重量与Hamming距离之间的变换关系以及它们与游程之间的联系,获得了一系列重要的推论。Abstract: The relation between weight and sidelobes of cross-correlation function and the relations between Hamming distance and numbers in a sequence are systematically studied in this paper. And then the general-purpose weight theorem and Hamming distance theorems are proved. Furthernmore, the transformation relations of weights, Hamming distances between the orthogonal codes,complementary codes, and the code pair of standard orthogonal transformation in the procedure of Tseng dissolving, and the association between them and runs are studied. And then, a series of importance corollarys are obtained.
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Shannon C E. A mathematical theory of communication, Bell Sys. Tech. J., 1948, 27(3): 379-423; 27(4): 623-656.[2]杨光正.脉压码时间旁瓣特性的研究.电子科学学刊,1994, 16(1): 40-48.[3]杨光正,杨翔宇,徐丽娟.二进制序列的群相关特性.电子科学学刊,1997, 19(2): 158-165.[4]杨光正,杨翔宇,徐丽娟.二进制序列的游程相关函数.电子科学学刊,1998,20(3): 342-351.[5]杨光正,杨翔宇,徐丽娟.二进制序列的Tseng游程定理.电子科学学刊,1998, 20(4): 500-507.[6]Golay M J E. Complementary series, IRE Trans[J].Inform. Theory.1961, 7(4):82-87[7]Tseng C-C, Liu C L. Complementary sets of sequences, IEEE Tans. on Inform. Thory, 1972, IT-18(5): 644-651.[8]Turyn R. Optimum codes study, Sylvania Electronic Systems, Sylvania Electric Products, Inc., Waltham, Mass: Final Rept., Jan. 1963, No.F437-1. -
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