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

@article{Hrmann2022ErrorErasureDO, title={Error-Erasure Decoding of Linearized Reed-Solomon Codes in the Sum-Rank Metric}, author={Felicitas H{\"o}rmann and Hannes Bartz and Sven Puchinger}, journal={2022 IEEE International Symposium on Information Theory (ISIT)}, year={2022}, pages={7-12} }

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 by incorporating erasures into the known syndrome-based…

## 2 Citations

### Multilayer crisscross error and erasure correction

- Computer ScienceArXiv
- 2022

In this work, multilayer crisscross error and erasures are considered, which affect entire rows and columns in the matrices of a list of matrices, and the multi-cover metric is introduced.

### Covering Properties of Sum-Rank Metric Codes

- Computer Science2022 58th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
- 2022

This work intends to answer the question: what is the minimum cardinality of a code given a sum-rank covering radius, and shows the relations of this quantity between different metrics and provides several lower and upper bounds for sum-Rank metric codes.

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