New Minimum Storage Regenerating Codes With Small Sub-packetization Levels for All Admissible Repair Degrees
Abstract
In this paper, {we propose a new family of $(n, k)$ Minimum Storage Regenerating (MSR) codes} for distributed storage systems. By structuring the parity-check matrix as a block Vandermonde matrix composed of diagonal matrices and generalized permutation matrices, the proposed code achieves a sub-packetization level of N = (d−k+1)⌈n/2⌉ and supports any repair degree k+1≤ d<n. A key innovation of the new construction lies in relaxing the strict commutativity condition previously required for the building blocks in the parity-check matrices of Ye-Barg codes. We introduce a novel proof technique to establish the MDS property without relying on full commutativity, thereby generalizing the applicability of block Vandermonde matrices and enriching the family of Ye-Barg codes. Additionally, the sparsity of the parity-check matrix enhances encoding and decoding efficiency by reducing computational complexity. This work provides new insights into the construction of MSR codes.
Related
- Exact Storage-Repair-Bandwidth Tradeoffs for (6,5,5) and (7,6,6) Exact-Repair Regenerating Codes
- Exact Minimum Extension Degrees for Reed Solomon Codes under Linear and Nonlinear Repair at the Cut Set Bound
- Random walk in a regenerating random environment
- Fusion rules and rigidity for weight modules over the simple admissible affine sl(2) and N=2 superconformal vertex operator superalgebras
- Classical freeness of affine vertex algebras of sl2 at boundary admissible levels
BibTeX
@misc{li2026minimum,
title = {{New Minimum Storage Regenerating Codes With Small Sub-packetization Levels for All Admissible Repair Degrees}},
author = {Jie Li and Xiaohu Tang and Linqi Song},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15329},
eprint = {2610.15329},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15329},
}
RIS
TY - UNPB
TI - New Minimum Storage Regenerating Codes With Small Sub-packetization Levels for All Admissible Repair Degrees
AU - Jie Li
AU - Xiaohu Tang
AU - Linqi Song
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15329
UR - https://arxiv.org/abs/2610.15329
AB - In this paper, {we propose a new family of $(n, k)$ Minimum Storage Regenerating (MSR) codes} for distributed storage systems. By structuring the parity-check matrix as a block Vandermonde matrix composed of diagonal matrices and generalized permutation matrices, the proposed code achieves a sub-packetization level of N = (d−k+1)^⌈n/2⌉ and supports any repair degree k+1≤ d<n. A key innovation of the new construction lies in relaxing the strict commutativity condition previously required for the building blocks in the parity-check matrices of Ye-Barg codes. We introduce a novel proof technique to establish the MDS property without relying on full commutativity, thereby generalizing the applicability of block Vandermonde matrices and enriching the family of Ye-Barg codes. Additionally, the sparsity of the parity-check matrix enhances encoding and decoding efficiency by reducing computational complexity. This work provides new insights into the construction of MSR codes.
ER -