關(guān)于線性分組碼的不可檢錯誤概率
ON UNDETECTABLE ERROR PROBABILITIES OF LINEAR BLOCK CODES
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摘要: 本文給出了檢錯好碼的定義,證明了GF(2)上的(n,k)線性分組碼為檢錯好碼的充要條件是其對偶碼也為檢錯好碼。文中還得到了關(guān)于檢錯好碼的一系列新的結(jié)果。對二元(n,k)線性分組碼,我們給出了不可檢錯誤概率新的下限。這些限只與n和k有關(guān),而與碼的重量結(jié)構(gòu)無關(guān)。
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關(guān)鍵詞:
- 信息論; 線性分組碼; 對偶碼; 不可檢錯誤概率; 檢錯好碼
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. -
林舒, 科斯特洛著,王育民,王新梅譯,差錯控制編碼基礎(chǔ)和應(yīng)用,人民郵電出版社,北京,1989年,第15-16頁.[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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