Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	郑大彬教授，湖北大学
Inviter:	陈绍示
Title:	Generalized Hamming weights of linear codes from quadratic forms over finite fields of even characteristic
Language:	Chinese
Time & Venue:	2024.01.30 15:00-16:00 思源楼525
Abstract:	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 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 sub-spaces of the field, and complement the results of Li and Li.