1 citations · 1 across the 6 of their papers we have counts for
8 papers
On the structure of polynomial ideal codes and additive Reed--Solomon codes
Umberto Martínez-Peñas, Rubén Rodríguez-Ballesteros
We study structural properties of polynomial ideal (PI) codes and additive Reed--Solomon (aRS) codes in the folded Hamming metric (equivalently, the Hamming metric over a larger al…
Upper bounds on the length of quasi-MDS codes
Umberto Martínez-Peñas, Rubén Rodríguez-Ballesteros
We study upper bounds on the length of -linear QMDS codes in the folded Hamming distance relative to their other parameters, especially the field size . Via a corre…
Linear codes in the folded Hamming distance and the quasi MDS property
Umberto Martínez-Peñas, Rubén Rodríguez-Ballesteros
In this work, we study linear codes with the folded Hamming distance, or equivalently, codes with the classical Hamming distance that are linear over a subfield. This includes addi…
New constructions of MSRD codes
Umberto Martínez-Peñas
In this work, we provide four methods for constructing new maximum sum-rank distance (MSRD) codes. The first method, a variant of cartesian products, allows faster decoding than kn…
Distributed matrix multiplication with straggler tolerance using algebraic function fields
Adrián Fidalgo-Díaz, Umberto Martínez-Peñas
The problem of straggler mitigation in distributed matrix multiplication (DMM) is considered for a large number of worker nodes and a fixed small finite field. Polynomial codes and…
Integer sequences that are generalized weights of a linear code
Elisa Gorla, Elisa Lorenzo García, Umberto Martínez-Peñas +1
Which integer sequences are sequences of generalized weights of a linear code? In this paper, we answer this question for linear block codes, rank-metric codes, and more generally…
Sum-rank metric codes
Elisa Gorla, Umberto Martínez-Peñas, Flavio Salizzoni
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 co…
Doubly and triply extended MSRD codes
Umberto Martínez-Peñas
In this work, doubly extended linearized Reed--Solomon codes and triply extended Reed--Solomon codes are generalized. We obtain a general result in which we characterize when a mul…