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 tF
full errors, tR row erasures and tC column erasures up to 2tF+tR+tC≤n−k in the sum-rank metric requiring at most O(n2)
operations in Fqm, 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.Comment: 6 pages, presented at ISIT 202