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

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 $2t_F+t_R+t_C\le n-k$ in the sum-rank metric requiring at most $\mathcal{O}(n^2)$ operations in ${\mathbb{F}}_{q^m}$, 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.

6 pages, presented at ISIT 2022

References in corpus (1)

• Residues of skew rational functions

Cited by in corpus (1)

• Fast Decoding of Interleaved Linearized Reed-Solomon Codes and Variants