7 papers
Systematic Maximum Sum Rank Codes
Paulo Almeida, Umberto Martínez-Penas, Diego Napp
In the last decade there has been a great interest in extending results for codes equipped with the Hamming metric to analogous results for codes endowed with the rank metric. This…
Hamming and simplex codes for the sum-rank metric
Umberto Martínez-Peñas
Sum-rank Hamming codes are introduced in this work. They are essentially defined as the longest codes (thus of highest information rate) with minimum sum-rank distance at least $ 3…
Locally Repairable Convolutional Codes with Sliding Window Repair
Umberto Martínez-Peñas, Diego Napp
Locally repairable convolutional codes (LRCCs) for distributed storage systems (DSSs) are introduced in this work. They enable local repair, for a single node erasure (or more gene…
Universal and Dynamic Locally Repairable Codes with Maximal Recoverability via Sum-Rank Codes
Umberto Martínez-Peñas, Frank R. Kschischang
Locally repairable codes (LRCs) are considered with equal or unequal localities, local distances and local field sizes. An explicit two-layer architecture with a sum-rank outer cod…
Theory of supports for linear codes endowed with the sum-rank metric
Umberto Martínez-Peñas
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-multi…
Reliable and Secure Multishot Network Coding using Linearized Reed-Solomon Codes
Umberto Martínez-Peñas, Frank R. Kschischang
Multishot network coding is considered in a worst-case adversarial setting in which an omniscient adversary with unbounded computational resources may inject erroneous packets in u…