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The generalized Hamming weight of linear codes is a natural generalization ofthe minimum Hamming distance. They convey the structural information of alinear code and determine its performance in various applications, and havebecome one of important research topics in coding theory. Recently, Li (IEEETrans. 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 aquadratic form over a finite field of odd characteristic by analysis of thesolutions of the restricted quadratic equation in its subspace. In this paper,we further determine the complete weight hierarchy of linear codes from aquadratic form over a finite field of even characteristic by carefully studyingthe behavior of the quadratic form on the subspaces of this field and its dualspace, and complement the results of Li and Li.

Generalized Hamming Weights of Linear Codes from Quadratic Forms over Finite Fields of Even Characteristic