Codes in the sum-rank metric: Fundamentals and applications

U Martínez-Peñas, M Shehadeh… - … and Trends® in …, 2022 - nowpublishers.com
Codes in the sum-rank metric have attracted significant attention for their applications in
distributed storage systems, multishot network coding, streaming over erasure channels …

Reed-Solomon coding algorithms based on Reed-Muller transform for any number of parities

L Yu, SJ Lin, H Hou, Z Li - IEEE Transactions on Computers, 2023 - ieeexplore.ieee.org
Based on the Reed-Muller (RM) transform, this paper proposes a Reed-Solomon (RS)
encoding/erasure decoding algorithm for any number of parities. Specifically, we first …

Eigenvalue bounds for sum-rank-metric codes

A Abiad, AP Khramova… - IEEE Transactions on …, 2023 - ieeexplore.ieee.org
We consider the problem of deriving upper bounds on the parameters of sum-rank-metric
codes, with focus on their dimension and block length. The sum-rank metric is a combination …

Optimal anticodes, MSRD codes, and generalized weights in the sum-rank metric

E Camps-Moreno, E Gorla, C Landolina… - IEEE Transactions …, 2022 - ieeexplore.ieee.org
Sum-rank metric codes have recently attracted the attention of many researchers, due to
their relevance in several applications. Mathematically, the sum-rank metric is a natural …

Fast decoding of interleaved linearized Reed-Solomon codes and variants

H Bartz, S Puchinger - arXiv preprint arXiv:2201.01339, 2022 - arxiv.org
We construct $ s $-interleaved linearized Reed--Solomon (ILRS) codes and variants and
propose efficient decoding schemes that can correct errors beyond the unique decoding …

Error-erasure decoding of linearized Reed-Solomon codes in the sum-rank metric

F Hörmann, H Bartz, S Puchinger - 2022 IEEE International …, 2022 - ieeexplore.ieee.org
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) …

Efficient decoding of folded linearized reed-solomon codes in the sum-rank metric

F Hörmann, H Bartz - arXiv preprint arXiv:2109.14943, 2021 - arxiv.org
Recently, codes in the sum-rank metric attracted attention due to several applications in eg
multishot network coding, distributed storage and quantum-resistant cryptography. The sum …

A linear programming bound for sum-rank metric codes

A Abiad, AL Gavrilyuk, AP Khramova… - IEEE Transactions …, 2024 - ieeexplore.ieee.org
A linear programming bound for sum-rank metric codes Page 1 IEEE TRANSACTIONS ON
INFORMATION THEORY, VOL. X, NO. Y, MONTH YYYY 1 A linear programming bound for …

Support-Guessing Decoding Algorithms in the Sum-Rank Metric

T Jerkovits, H Bartz, A Wachter-Zeh - arXiv preprint arXiv:2410.15806, 2024 - arxiv.org
The sum-rank metric generalizes the Hamming and rank metric by partitioning vectors into
blocks and defining the total weight as the sum of the rank weights of these blocks, based on …

Sum-rank metric codes

E Gorla, U Martínez-Peñas, F Salizzoni - arXiv preprint arXiv:2304.12095, 2023 - arxiv.org
Sum-rank metric codes are a natural extension of both linear block codes and rank-metric
codes. They have several applications in information theory, including multishot network …