Weight hierarchy of a class of linear codes relating to non-degenerate quadratic forms

TL;DR

This paper determines the generalized Hamming weights of a specific class of linear codes linked to non-degenerate quadratic forms, advancing understanding of their weight hierarchy through analysis of quadratic forms over finite fields.

Contribution

It provides a complete solution for the generalized Hamming weights of these codes, connecting quadratic form properties with code weight hierarchies.

Findings

All generalized Hamming weights are explicitly calculated.

Results reveal the structure of subspaces related to quadratic forms.

The study enhances the theoretical understanding of code weight hierarchies.

Abstract

In this paper, we discuss the generalized Hamming weights of a class of linear codes associated with non-degenerate quadratic forms. In order to do so, we study the quadratic forms over subspaces of finite field and obtain some interesting results about subspaces and their dual spaces. On this basis, we solve all the generalized Hamming weights of these linear codes.