Generalized Hamming Weights of Linear Codes From Quadratic Forms Over Finite Fields of Even Characteristic

被引：2

作者：

Liu C. ^{[1
]}

Zheng D. ^{[1
]}

Wang X. ^{[1
]}

机构：

[1] Hubei University, Hubei Province Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Wuhan

来源：

IEEE Trans. Inf. Theory | 2023年 / 9卷 / 5676-5686期

基金：

中国国家自然科学基金;

关键词：

Generalized Hamming weight; linear code; quadratic form; weight hierarchy;

D O I：

10.1109/TIT.2023.3277454

中图分类号：

学科分类号：

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 (2021) and Li and Li (2022) obtained the complete weight hierarchy of linear codes from quadratic forms over finite fields 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 quadratic forms over finite fields of even characteristic by carefully studying the behavior of the corresponding restricted quadratic forms to the subspaces of the field, and complement the results of Li and Li. © 1963-2012 IEEE.

引用

页码：5676 / 5686

页数：10

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