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 …

Reliable and secure multishot network coding using linearized Reed-Solomon codes

U Martínez-Peñas… - IEEE Transactions on …, 2019 - ieeexplore.ieee.org
Multishot network coding is considered in a worst-case adversarial setting in which an
omniscient adversary with unbounded computational resources may inject erroneous …

Theory of supports for linear codes endowed with the sum-rank metric

U Martínez-Peñas - Designs, Codes and Cryptography, 2019 - Springer
The sum-rank metric naturally extends both the Hamming and rank metrics in coding theory
over fields. It measures the error-correcting capability of codes in multishot matrix …

[HTML][HTML] Sum-rank product codes and bounds on the minimum distance

GN Alfarano, FJ Lobillo, A Neri… - Finite Fields and Their …, 2022 - Elsevier
The tensor product of one code endowed with the Hamming metric and one endowed with
the rank metric is analyzed. This gives a code which naturally inherits the sum-rank metric …

Sum-rank BCH codes and cyclic-skew-cyclic codes

U Martínez-Peñas - IEEE Transactions on Information Theory, 2021 - ieeexplore.ieee.org
In this work, cyclic-skew-cyclic codes and sum-rank BCH codes are introduced. Cyclic-skew-
cyclic codes are characterized as left ideals of a suitable non-commutative finite ring …

Construction and fast decoding of binary linear sum-rank-metric codes

H Chen, Y Qi, Z Cheng - arxiv preprint arxiv:2311.03619, 2023 - arxiv.org
Sum-rank-metric codes have wide applications in the multishot network coding and the
distributed storage. Linearized Reed-Solomon codes, sum-rank BCH codes and their Welch …

New explicit good linear sum-rank-metric codes

H Chen - IEEE Transactions on Information Theory, 2023 - ieeexplore.ieee.org
Sum-rank-metric codes have wide applications in universal error correction, multishot
network coding, space-time coding and the construction of partial-MDS codes for repair in …

Cyclic and negacyclic sum-rank codes

H Chen, C Ding, Z Cheng, C **e - arxiv preprint arxiv:2401.04885, 2024 - arxiv.org
Sum-rank codes have known applications in the multishot network coding, the distributed
storage and the construction of space-time codes. U. Mart\'{\i} nez-Pe\~{n} as introduced the …

Covering Codes, List-Decodable Codes and Strong Singleton-Like Bounds in the Sum-Rank Metric

H Chen - arxiv preprint arxiv:2311.07831, 2023 - arxiv.org
Codes in the sum-rank metric have received many attentions in recent years, since they
have wide applications in multishot network coding, space-time coding and distributed …

Some matroids related to sum-rank metric codes

A Panja, R Pratihar, TH Randrianarisoa - Discrete Mathematics, 2023 - Elsevier
We introduce the notion of sum-matroids and show its association with sum-rank metric
codes. As a consequence, some results for sum-rank metric codes by Martínez-Peñas are …