广义Hamming重量和等重码
GENERALIZED HAMMING WEIGHTS AND CONSTANT WEIGHT CODES
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摘要: 本文将线性码的广义Hamming重量的概念推广到非线性码上去,并导出了一种广义Elias界.对于线性等重码,本文给出了其完整的重量谱系.Abstract: This paper generalizes the definition of generalized Hamming weights for linear codes to nonlinear codes, derives a generalized Elias bound, and gives the weight hierarchy of linear constant weight codes.
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Wei V K. Generalized Hamming weights for linear codes. IEEE Trans. on IT, 1991, IT-37(5): 1412-1418.(2J Wei V K, et al. On the generalized Hamming weights of product codes. IEEE Trans. on IT, 1993, IT-39(5): 1709-1713.[2](3J Helleseth H, et al. Bounds on the minimum support weights. IEEE Trans. on IT, 1995, IT-41(2): 432-439.[3]Yang K, et al. On the weight hierarchy of geometric Goppa codes. IEEE Trans. on IT, 1994, IT-40(3): 913-920.[4]MacWilliams F J, Sloane N J A. The Theory of Error-Correcting Codes. Amsterdam, North-Holland publish company, 1977, Chapter 1, Chapter 17.[5]Elias P. Error-free coding, IEEE Trans. on IT, 1954, IT-4(1): 29-37.[6]王新梅.最佳(n,2,w)二进制等重检错码的存在性及其猜想.中国科学,1987, 17(11): 1225-1232.[7]杨义先,胡正名.线性等重码的结构分析.电子学报,1990, 18(6): 1-8. -
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