generalized Hamming weight, weight hierarchy, linear code, difference sequence, finite projective geometry
The weight hierarchy of a [n,k;q] linear code C over Fq is the sequence (d1,⋯,dr,⋯,dk), where dr is the smallest support weight of an r-dimensional subcode of C. In this paper, by using the finite projective geometry method, we research a class of weight hierarchy of linear codes with dimension 5. We first find some new pre-conditions of this class. Then we divide its weight hierarchies into six subclasses, and research one subclass to determine nearly all the weight hierarchies of this subclass of weight hierarchies of linear codes with dimension 5.
Tsinghua University Press
Guoxiang Hu, Huanguo Zhang, Lijun Wang et al. A Class of the Hamming Weight Hierarchy of Linear Codes with Dimension 5. Tsinghua Science and Technology 2014, 19(05): 442-451.