  The generalized Hamming weight of linear codes is a natural generalization of
the minimum Hamming distance. They convey the structural information of a
linear code and determine its performance in various applications, and have
become one of important research topics in coding theory. Recently, Li (IEEE
Trans. Inf. Theory, 67(1): 124-129, 2021) and Li and Li (Discrete Math., 345:
112718, 2022) obtained the complete weight hierarchy of linear codes from a
quadratic form over a finite field of odd characteristic by analysis of the
solutions of the restricted quadratic equation in its subspace. In this paper,
we further determine the complete weight hierarchy of linear codes from a
quadratic form over a finite field of even characteristic by carefully studying
the behavior of the quadratic form on the subspaces of this field and its dual
space, and complement the results of Li and Li.
