关于线性分组码的不可检错误概率
ON UNDETECTABLE ERROR PROBABILITIES OF LINEAR BLOCK CODES
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摘要: 本文给出了检错好码的定义,证明了GF(2)上的(n,k)线性分组码为检错好码的充要条件是其对偶码也为检错好码。文中还得到了关于检错好码的一系列新的结果。对二元(n,k)线性分组码,我们给出了不可检错误概率新的下限。这些限只与n和k有关,而与码的重量结构无关。Abstract: The definition of good codes for error detection is given- It is proved that linear block codes in GF(q) are good codes for error detection if and only if its dual codes are good ones also- A series of new results abour good codes for error detection is derived. New lower bounds on undetectable error probabilities of binary (n,k) linear block codes are obtained, which have no relation to the weight structure of the codes but only to n and k.
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林舒, 科斯特洛著,王育民,王新梅译,差错控制编码基础和应用,人民邮电出版社,北京,1989年,第15-16页.[2]T. Kassmi, T. Klove, S. Lin, IEEE Trans. on IT, IT-19(1983)1, 131-136.[3]J. K. Wolf, A. H. Michelson, A. H. Levesque, IEEE Trans. on COM, COM-30(1982)2, 317-324.[4]F. J. Macwilliams, N. J. A. Sloane, The theory of error-correcting codes, Amsterdam: North-Holland, (1977), pp. 225-232.[5]S. K. Leung-Yan-Cheong, M. E. Hellman, IEEE Trans. on IT, IT-22(1976)2, 235-237.[6]S. K. Lenng-Yan-Cheong, E. R. Barnes, D. U. Friedman, IEEE Trans. on IT, IT-25(1979)1, 110-112.[7]T. Kassmi, S. Lin, IEEE Trans. on COM, COM-32(1984)9, 998-1006.[8]P. Perry, IEEE. Trans. on IT, IT-37(1991)2, 375-378.[9]R. J. McEliece, The theory of information and coding, Addison-Wesley, Reading, Mass., (1977), pp. 245-249. -
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