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Efficient Decoding of Folded Linearized Reed-Solomon Codes in the Sum-Rank Metric

Hörmann, Felicitas and Bartz, Hannes (2022) Efficient Decoding of Folded Linearized Reed-Solomon Codes in the Sum-Rank Metric. WCC 2022: The Twelfth International Workshop on Coding and Cryptography, March 7 - 11, 2022, Rostock, Germany (virtual). doi: 10.48550/arXiv.2109.14943.

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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 O(sn^2) operations in F_{q^m}, where s<=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.

Item URL in elib:https://elib.dlr.de/146410/
Document Type:Conference or Workshop Item (Speech)
Title:Efficient Decoding of Folded Linearized Reed-Solomon Codes in the Sum-Rank Metric
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Hörmann, FelicitasUNSPECIFIEDhttps://orcid.org/0000-0003-2217-9753UNSPECIFIED
Bartz, HannesUNSPECIFIEDhttps://orcid.org/0000-0001-7767-1513UNSPECIFIED
Date:March 2022
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In ISI Web of Science:No
Keywords:folded linearized Reed-Solomon codes, sum-rank metric, interpolation-based decoding, list decoding, probabilistic unique decoding
Event Title:WCC 2022: The Twelfth International Workshop on Coding and Cryptography
Event Location:Rostock, Germany (virtual)
Event Type:international Conference
Event Dates:March 7 - 11, 2022
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Communication, Navigation, Quantum Technology
DLR - Research area:Raumfahrt
DLR - Program:R KNQ - Communication, Navigation, Quantum Technology
DLR - Research theme (Project):R - Project Cybersecurity for Autonomous and Networked Systems [KNQ]
Location: Oberpfaffenhofen
Institutes and Institutions:Institute of Communication and Navigation > Satellite Networks
Deposited By: Hörmann, Felicitas
Deposited On:16 Feb 2022 12:18
Last Modified:24 Jan 2023 18:31

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