Maximum-sum-rank distance (MSRD) code[1]
Alternative Names: Optimal sum-rank-distance code.
Description
A sum-rank-metric code whose parameters satisfy the sum-rank-metric Singleton bound with equality.
An \([n\times m,k,d]_q\) code is MSRD if its 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.
Cousins
- Maximum distance separable (MDS) code— MSRD codes generalize MDS codes from the Hamming metric to the sum-rank metric.
- Maximum-rank distance (MRD) code— MSRD codes generalize MRD codes from the rank metric to the sum-rank metric.
Member of code lists
Primary Hierarchy
Parents
Maximum-sum-rank distance (MSRD) code
Children
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
Page edit log
- Victor V. Albert (2026-06-08) — most recent
- Victor V. Albert (2024-08-15)
Cite as:
“Maximum-sum-rank distance (MSRD) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/maximum_sum_rank_distance, arXiv:2606.11484