Error-Erasure Decoding of Linearized Reed-Solomon Codes in the Sum-Rank Metric
release_r3yru5aixvbbhcp2dmukda646u
by
Felicitas Hörmann, Hannes Bartz, Sven Puchinger
2022
Abstract
Codes in the sum-rank metric have various applications in error control for
multishot network coding, distributed storage and code-based cryptography.
Linearized Reed-Solomon (LRS) codes contain Reed-Solomon and Gabidulin codes as
subclasses and fulfill the Singleton-like bound in the sum-rank metric with
equality. We propose the first known error-erasure decoder for LRS codes to
unleash their full potential for multishot network coding. The presented
syndrome-based Berlekamp-Massey-like error-erasure decoder can correct t_F
full errors, t_R row erasures and t_C column erasures up to 2t_F + t_R +
t_C ≤ n-k in the sum-rank metric requiring at most 𝒪(n^2)
operations in 𝔽_q^m, where n is the code's length and k its
dimension. We show how the proposed decoder can be used to correct errors in
the sum-subspace metric that occur in (noncoherent) multishot network coding.
In text/plain
format
Archived Files and Locations
application/pdf 199.8 kB
file_o6tztglrwncajjlxcp7su6qr6a
|
arxiv.org (repository) web.archive.org (webarchive) |
2202.06758v1
access all versions, variants, and formats of this works (eg, pre-prints)