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Sum-rank-metric code[1]

Description

A code whose performance is evaluated in the sum-rank metric, which is a metric that generalizes both the Hamming metric and the rank metric.

Cousin

  • Binary code— The sum-rank metric generalizes both the Hamming metric and the rank metric [2].

Member of code lists

Primary Hierarchy

Classical Domain
Matrix Kingdom
Matrix-based codeECC
Parents
Matrix-based code
Distributed-storage codeECC
Sum-rank-metric codes are useful for distributed storage [3].
Sum-rank-metric code
Children
Rank-metric codeMRD
The sum-rank metric generalizes both the Hamming metric and the rank metric [2].
Maximum-sum-rank distance (MSRD) code

References

[1]
R. W. Nobrega and B. F. Uchoa-Filho, “Multishot Codes for Network Coding using Rank-Metric Codes”, (2010) arXiv:1001.2059
[2]
U. Martínez-Peñas, “Skew and linearized Reed-Solomon codes and maximum sum rank distance codes over any division ring”, (2018) arXiv:1710.03109
[3]
U. Martínez-Peñas and F. R. Kschischang, “Universal and Dynamic Locally Repairable Codes with Maximal Recoverability via Sum-Rank Codes”, (2019) arXiv:1809.11158
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Zoo Code ID: sum_rank_metric

Cite as:
“Sum-rank-metric code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/sum_rank_metric
BibTeX:
@incollection{eczoo_sum_rank_metric, title={Sum-rank-metric code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/sum_rank_metric} }
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Permanent link:
https://errorcorrectionzoo.org/c/sum_rank_metric

Cite as:

“Sum-rank-metric code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/sum_rank_metric

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/matrices/sum-rank-metric/sum_rank_metric.yml.