Efficient Decoding of Folded Linearized Reed-Solomon Codes in the Sum-Rank Metric
release_dd3yzncugffshmf7oq476peewi
by
Felicitas Hƶrmann, Hannes Bartz
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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