k维q元线性码的重量谱的分类

Classification of Weight Hierarchies of q-ary Linear Codes of Dimension k

为了研究"确定k维q元线性码几乎所有重量谱"这个难题,我们需要用Klφve的一组必要条件来引入重量谱的分类.易知类数f(f(k)=2^((k-2)(k-3)/2).本文得到了这些必要条件之间的关系,使得f(k)减少了很多.本文还用递推方法与含o,1元素的表格给出了描述每一类的必要条件.

In order to study the difficult problem on “determing almost all weight hier- archies of q-ary linear codes of dimension k”, we need introduce a classification of weight hierarchies by Klove＇s a group of necessary conditions. It is easy to see that the number of classes f（k） = 2^（k-2）（k-3）/2. In this paper, the relations between these necessary conditions was obtained, such that f（k） has decreased very much, the necessary conditions described each class also was given by recursive method and tables contained 0, 1 elements.