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

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.

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References in corpus (3)

• Complete Weight Enumerators of a Family of Three-Weight Linear Codes
• Generalized Hamming weights of three classes of linear codes
• A class of cyclotomic linear codes and their generalized Hamming weights

Cited by in corpus (2)

• Weight hierarchies and weight distributions of a familiy of $p$-ary linear codes
• Weight hierarchies of a family of linear codes associated with degenerate quadratic forms