Maximum-sum-rank distance (MSRD) code[1] 

Also known as Optimal sum-rank-distance code.

Description

An \([n\times m,k,d]_q\) rank-metric code whose parameters are such that the sum-rank-metric Singleton bound [1; Prop. 34] \begin{align} d_{\text{SR}}(C) \leq n - k + 1 \tag*{(1)}\end{align} becomes an equality, where \(d_{\text{SR}}\) is the sum-rank metric.

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References

[1]
U. Martínez-Peñas, “Skew and linearized Reed-Solomon codes and maximum sum rank distance codes over any division ring”, (2018) arXiv:1710.03109
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Zoo Code ID: maximum_sum_rank_distance

Cite as:
“Maximum-sum-rank distance (MSRD) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/maximum_sum_rank_distance
BibTeX:
@incollection{eczoo_maximum_sum_rank_distance, title={Maximum-sum-rank distance (MSRD) code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/maximum_sum_rank_distance} }
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Cite as:

“Maximum-sum-rank distance (MSRD) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/maximum_sum_rank_distance

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