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Efficient Decoding of Folded Linearized Reed-Solomon Codes in the Sum-Rank Metric
- Publication Year :
- 2021
- Publisher :
- arXiv, 2021.
-
Abstract
- Recently, codes in the sum-rank metric attracted attention due to several applications in e.g. multishot network coding, distributed storage and quantum-resistant cryptography. The sum-rank analogs of Reed-Solomon and Gabidulin codes are linearized Reed-Solomon codes. We show how to construct $h$-folded linearized Reed-Solomon (FLRS) codes and derive an interpolation-based decoding scheme that is capable of correcting sum-rank errors beyond the unique decoding radius. The presented decoder can be used for either list or probabilistic unique decoding and requires at most $\mathcal{O}(sn^2)$ operations in $\mathbb{F}_{q^m}$, where $s \leq h$ is an interpolation parameter and $n$ denotes the length of the unfolded code. We derive a heuristic upper bound on the failure probability of the probabilistic unique decoder and verify the results via Monte Carlo simulations.<br />Comment: 10 pages, 1 figure, presented at WCC 2022
- Subjects :
- interpolation-based decoding
FOS: Computer and information sciences
folded linearized Reed-Solomon codes
Computer Science - Information Theory
Information Theory (cs.IT)
sum-rank metric
Data_CODINGANDINFORMATIONTHEORY
list decoding
probabilistic unique decoding
Computer Science::Information Theory
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....2d0f8c10e4a789742a06e16b0356557b
- Full Text :
- https://doi.org/10.48550/arxiv.2109.14943