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

09/30/2021
by   Felicitas Hörmann, et al.
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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 analogues 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.

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