Work

Optimal Quantum ( r , δ )-Locally Repairable Codes From Matrix-Product Codes

Year: 2026

Type: article

Abstract: This paper studies optimal quantum $(r,δ)$-LRCs from matrix-product (MP) codes. We establish a necessary and sufficient condition for an MP code to be an optimal $(r,δ)$-LRC. Based on this, we present a characterization for optimal quantum $(r,δ)$-LRCs from MP codes with nested constituent codes, and also study optimal quantum $(r,δ)$-LRCs constructed from MP codes with non-nested constituent codes. Through Hermitian dual-containing and Euclidean dual-containing MP codes, we present five infinite families of optimal quantum $(r,δ)$-LRCs with flexible parameters.

Source: IEEE Transactions on Information Theory

DOI: 10.1109/tit.2026.3691784

Authors: Meng Cao, Kun Zhou

Institution: Beijing Institute of Mathematical Sciences and Applications

Language: English

Topic: Coding theory and cryptography

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Awards: G555335362, G740397416