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

@article{Hrmann2021EfficientDO, title={Efficient Decoding of Folded Linearized Reed-Solomon Codes in the Sum-Rank Metric}, author={Felicitas H{\"o}rmann and Hannes Bartz}, journal={ArXiv}, year={2021}, volume={abs/2109.14943} }

. Recently, codes in the sum-rank metric attracted attention due to several applications in e.g. multishot network coding, distributed storage and quantum-resistant cryptography. The sum-rank analogs of Reed–Solomon and Gabidulin codes are linearized Reed–Solomon codes. We show 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. The presented decoder can…

## 3 Citations

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

- Computer Science2022 IEEE International Symposium on Information Theory (ISIT)
- 2022

This work proposes 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 Berlekamp-Massey-like decoder.

### Fast Kötter-Nielsen-Høholdt Interpolation over Skew Polynomial Rings

- Computer ScienceIFAC-PapersOnLine
- 2022

A fast divide-and-conquer variant of K¨otter–Nielsen–Høholdt (KNH) interpolation algorithm that inputs a list of linear functionals on skew polynomial vectors, and outputs a reduced Gr¨obner basis of their kernel intersection and matches the previous best speeds for these tasks.

### 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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