Efficient Decoding of Folded Linearized Reed-Solomon Codes in the Sum-Rank Metric release_dd3yzncugffshmf7oq476peewi

by Felicitas Hƶrmann, Hannes Bartz

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2022  

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 š¯’Ŗ(sn^2) operations in š¯”½_q^m, where s ā‰¤ 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.
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Date   2022-02-14
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arXiv  2109.14943v2
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