域F_2上线性码的广义Rosenbloom-Tsfasman重量

Generalized Rosenbloom-Tsfasman weights for linear codes over F_2

受广义Hamming重量的启发,文章将极小RT重量看成是一个线性码的一维子码的一个极小性质,获得了一个高维RT重量的概念,它是广义Hamming重量的推广;得到了该广义重量的基本性质以及一些常见类型线性码关于该重量的值。

In light of the generalized Hamming weight, the minimum RT weight is viewed as a certain minimum property of one-dimensional subeodes, and a generalized notion of higher-dimensional RT weights is obtained,which is a generalization of generalized Hamming weights. Basic properties of the generalized weights are derived, and the values of these weights for well-known classes of codes are determined too.