Work

About the generalized Hamming weights of matrix-product codes

Year: 2025

Type: article

Abstract: We derive a general lower bound for the generalized Hamming weights of nested matrix-product codes, with a particular emphasis on the cases with two and three constituent codes. We also provide an upper bound which is reminiscent of the bounds used for the minimum distance of matrix-product codes. When the constituent codes are two Reed–Solomon codes, we obtain an explicit formula for the generalized Hamming weights of the resulting matrix-product code. We also deal with the non-nested case for the case of two constituent codes.

Source: Computational and Applied Mathematics

DOI: 10.1007/s40314-025-03141-x

Author: Rodrigo San-José

Institution: Universidad de Valladolid

Language: English

Topic: Coding theory and cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,390