8 research outputs found
Weight hierarchies of a family of linear codes associated with degenerate quadratic forms
We restrict a degenerate quadratic form over a finite field of odd
characteristic to subspaces. Thus, a quotient space related to is
introduced. Then we get a non-degenerate quadratic form induced by over the
quotient space. Some related results on the subspaces and quotient space are
obtained. Based on this, we solve the weight hierarchies of a family of linear
codes related to Comment: 12 page
The Weight Hierarchies of Linear Codes from Simplicial Complexes
The study of the generalized Hamming weight of linear codes is a significant
research topic in coding theory as it conveys the structural information of the
codes and determines their performance in various applications. However,
determining the generalized Hamming weights of linear codes, especially the
weight hierarchy, is generally challenging. In this paper, we investigate the
generalized Hamming weights of a class of linear code \C over \bF_q, which
is constructed from defining sets. These defining sets are either special
simplicial complexes or their complements in \bF_q^m. We determine the
complete weight hierarchies of these codes by analyzing the maximum or minimum
intersection of certain simplicial complexes and all -dimensional subspaces
of \bF_q^m, where 1\leq r\leq {\rm dim}_{\bF_q}(\C)