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Maximally recoverable (MR) code[1,2]

Alternative Names: Partial MDS code.

Description

A code with \((r,\delta)\) locality such that puncturing any \(\delta-1\) coordinates from each local \([r+\delta-1,r,\delta]\) code yields an MDS code.

Realizations

RAID storage [3].

Member of code lists

Primary Hierarchy

Classical Domain
Error-correcting code (ECC)
Block code
Distributed-storage codeECC
Code with locality
Parents
Code with locality
Maximally recoverable (MR) code

References

[1]
M. Blaum, J. L. Hafner, and S. Hetzler, “Partial-MDS Codes and their Application to RAID Type of Architectures”, (2014) arXiv:1205.0997
[2]
P. Gopalan, C. Huang, B. Jenkins, and S. Yekhanin, “Explicit Maximally Recoverable Codes with Locality”, (2013) arXiv:1307.4150
[3]
J. S. Plank and M. Blaum, “Sector-Disk (SD) Erasure Codes for Mixed Failure Modes in RAID Systems”, ACM Transactions on Storage 10, 1 (2014) DOI
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Zoo Code ID: maximally_recoverable

Cite as:
“Maximally recoverable (MR) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/maximally_recoverable, arXiv:2606.11484
BibTeX:
@incollection{eczoo_maximally_recoverable,
title={Maximally recoverable (MR) code},
booktitle={The Error Correction Zoo},
year={2026},
editor={Albert, Victor V. and Faist, Philippe},
eprint={2606.11484},
doi={10.48550/arXiv.2606.11484},
url={https://errorcorrectionzoo.org/c/maximally_recoverable}
}
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Permanent link:
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Cite as:

“Maximally recoverable (MR) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/maximally_recoverable, arXiv:2606.11484

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/properties/block/distributed_storage/lrc/maximally_recoverable.yml.