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．
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.
出处
《通信学报》
EI
CSCD
北大核心
1997年第7期75-78,共4页
Journal on Communications
基金
国家自然科学基金
关键词
对偶码
迹码
信通编码
generalized Hamming weight, dual code, trace code
