标题： 有限域上二次型的线性码的广义汉明权重 显示英文标题

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

摘要： 线性码的广义汉明重量是汉明距离的自然推广。它们传达了线性码的结构信息，并决定了其在各种应用中的性能，已成为编码理论中的重要研究课题。最近，Li（IEEE 传输 信息理论，67(1): 124-129, 2021）和 Li 与 Li（离散数学，345: 112718, 2022）通过分析其子空间中限制二次方程的解，从奇特征有限域上的二次型获得了线性码的完整重量层次。在本文中，我们通过仔细研究该域及其对偶空间中二次型在子空间上的行为，进一步确定了偶特征有限域上二次型的完整重量层次，并补充了 Li 与 Li 的结果。 显示英文摘要

摘要： 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.