Error-Erasure Decoding Strategies for Interleaved Linearized Reed-Solomon Codes

The sum-rank metric serves as a unifying framework for the prominent Hamming and rank metrics. In particular, the family of linearized Reed-Solomon (LRS) codes generalizes Reed-Solomon and Gabidulin codes while keeping the property of having the optimal unique decoding capability with respect to the sum-rank metric.

In this talk, we focus on the decoding of these codes with respect to an error-erasure setting, in which we allow errors as well as two types of erasures simultaneously. We present two different efficient error-erasure decoders for LRS codes and show that the decoding strategies are in fact two sides of the same coin. Further, we extend the consideration to vertically and horizontally interleaved LRS codes, whose additional structure allows the adapted decoders to decode far beyond the unique decoding radius with high probability.