Codes in the sum-rank metric: Fundamentals and applications
Codes in the sum-rank metric have attracted significant attention for their applications in
distributed storage systems, multishot network coding, streaming over erasure channels …
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 …
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 …
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
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 …
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 …
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 …
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 …
network coding, space-time coding and the construction of partial-MDS codes for repair in …
Cyclic and negacyclic sum-rank codes
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 …
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 …
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 …
codes. As a consequence, some results for sum-rank metric codes by Martínez-Peñas are …