Rank syndrome decoding
Syndrome decoding in the rank metric over F_(q^m); n, m, k and rank weight are separate parameters.
Classical · m = n · worst parameters
Extension degree m=n; worst decoding parameters in the source convention
Results
| # | PUBLICATION / AUTHORS | DATE | TIME BOUND | SPACE BOUND | EVIDENCE |
|---|---|---|---|---|---|
| 1 | Rank Syndrome Decoding Estimator - An Asymptotic and Concrete AnalysisePrint 2026/082SourceBibTeX / details | 19 Jan 2026 | 20.1481 n² + o(n²) | — | PreprintSource checked |
Comparison definition & assumptions
- Regime
- Extension degree m=n; worst decoding parameters in the source convention
- Computation
- Classical
- Rigor
- Source asymptotic analysis
- Instances
- Random rank-metric codes
- Cost scale
- 2^{c n² + o(n²)}
- Parameter
- n²
- Description
- Square-regime rank-decoding baseline.
- Comparison rules
- Use the n² exponential scale. This is the source’s worst-parameter baseline for m=n, not a Hamming-decoding exponent or an assertion of optimality among all algorithms.
- Tags
- rank metric, m=n, quadratic exponent