Work

Complete weight enumerators and weight hierarchies of two classes of linear codes

Year: 2025

Type: article

Abstract: The study of generalized Hamming weights for linear coding is an important area of research in coding theory as it provides valuable structural information about coding and plays a crucial role in determining the performance of coding in various applications. In this paper, two distinct classes of linear codes are devised through the selection of two particular defining sets. Initially, the weight distributions of these codes are ascertained. Subsequently, by conducting a detailed analysis of the intersections between the defining sets and the duals of all r -dimensional subspaces, the complete weight hierarchies of the two classes of linear codes are successfully determined.

Source: Discrete Mathematics

DOI: 10.1016/j.disc.2025.114510

Authors: Jiawei He, Yinjin Liao

Institution: Nanchang Hangkong University

Language: English

Topic: Coding theory and cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,320

Funders: Nanchang Hangkong University, Ministry of Education of the People's Republic of China, Central China Normal University