二進制序列的重只定理和Hamming距離定理
WEIGHT THEOREM AND HAMMING DISTANCE THEOREMS OF BINARY SEQUENCES
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摘要: 本文系統(tǒng)地研究了二進制序列的重量與互相關函數(shù)旁瓣之和的關系,Hamming距離與游程數(shù)之間的關系,證明了普適的重量定理和Hamming距離定理,在此基礎上,進一步研究了標準正交變換,正交碼、互補碼在Tseng分解過程中的重量與Hamming距離之間的變換關系以及它們與游程之間的聯(lián)系,獲得了一系列重要的推論。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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