# Decoding of Interleaved Linearized Reed-Solomon Codes with Applications to Network Coding

@article{Bartz2021DecodingOI, title={Decoding of Interleaved Linearized Reed-Solomon Codes with Applications to Network Coding}, author={Hannes Bartz and Sven Puchinger}, journal={2021 IEEE International Symposium on Information Theory (ISIT)}, year={2021}, pages={160-165} }

Recently, Martínez-Peñas and Kschischang (IEEE Trans. Inf. Theory, 2019) showed that lifted linearized Reed-Solomon codes are suitable codes for error control in multishot network coding. We show how to construct and decode lifted interleaved linearized Reed-Solomon codes. Compared to the construction by Martínez-Peñas-Kschischang, interleaving allows to increase the decoding region significantly (especially w.r.t. the number of insertions) and decreases the overhead due to the lifting (i.e…

## 4 Citations

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

- Computer ScienceArXiv
- 2022

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 sumrank metric requiring at most O(n) operations in Fqm.

Optimal Anticodes, MSRD Codes, and Generalized Weights in the Sum-Rank Metric

- Computer ScienceIEEE Transactions on Information Theory
- 2022

It is proved that the generalized weights of an MSRD code are determined by its parameters, which explains how generalized weights measure information leakage in multishot network coding.

The non-GRS properties for the twisted generalized Reed-Solomon code and its extended code

- Computer ScienceArXiv
- 2022

It is proved that almost all ofTGRS codes and extended TGRS codes are non-GRS when the code rate more than one half.

Efficient Decoding of Folded Linearized Reed-Solomon Codes in the Sum-Rank Metric

- Computer ScienceArXiv
- 2021

This work shows how to construct h-folded linearized Reed–Solomon (FLRS) codes and derive an interpolation-based decoding scheme that is capable of correcting sum-rank errors beyond the unique decoding radius and derives a heuristic upper bound on the failure probability of the probabilistic unique decoder.

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