| 广义Hamming重量上,下界的对偶定理 |
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| 引用本文： | 岳殿武,胡正名.广义Hamming重量上,下界的对偶定理[J].通信学报,1997,18(7):75-78. |
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| 作者姓名： | 岳殿武 胡正名 |
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| 作者单位： | 南京邮电学院电信工程系(岳殿武)，北京邮电大学信息工程系(胡正名) |
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| 摘 要： | 本文给出了一种广义Ｈａｍｍｉｎｇ重量上、下界的对偶定理。即若给定一个码的对偶码的广义Ｈａｍｍｉｎｇ重量上界（或者下界），可以给出该码的广义Ｈａｍｍｉｎｇ重量上界（或者下界）。Ｈ．Ｓｔｉｃｈ－ｎｏｔｈ（１９９４）曾给出了迹码（如ＢＣＨ码和Ｇｏｐｐａ码的对偶码）的广义Ｈａｍｍｉｎｇ重量一种上、下界，如果采用本文结果就可以给出迹码的对偶码的广义Ｈａｍｍｉｎｇ重量一种上、下界。因此，本文的结果是Ｈ．Ｓｔｉｃｈｎｏｔｈ的结果的有益补充
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| 关 键 词： | 广义Hamming重量 对偶码 迹码 |
A Dual Theorem of Upper and Lower Bounds on the Generalized Hamming Weights |
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| Yue Dianwu.A Dual Theorem of Upper and Lower Bounds on the Generalized Hamming Weights[J].Journal on Communications,1997,18(7):75-78. |
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| Authors: | Yue Dianwu |
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| Abstract: | A dual theorem of upper and lower bounds on the generalized Hamming weights is obtained. This means that if upper bounds (or lower bounds) have been known for the generalized Hamming weights of the dual of a given code, upper bounds (or lower bounds) for generalized Hamming weights of this code can be given. H.Stichtenoth (1994) gave sharp bounds for the generalied Hamming weights of trace codes (such as duals of BCH codes and classial Goppa codes). By the above mentioned dual theorem, sharp bounds for the generalied Hamming weights of duals of trace codes (such as BCH codes and classical Goppa codes) can be also derived. Therefore our result is complementary to H.Stichtenoth' result. |
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| Keywords: | generalized Hamming weight dual code trace code |
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