Error-Erasure Decoding of Linearized Reed-Solomon Codes in the Sum-Rank Metric
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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.
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