44 citations · 62 across the 6 of their papers we have counts for
10 papers
Constructing Partial MDS Codes from Reducible Curves
Tristram Bogart, Anna-Lena Horlemann-Trautmann, David Karpuk +2
We propose reducible algebraic curves as a mechanism to construct Partial MDS (PMDS) codes geometrically. We obtain new general existence results, new explicit constructions and im…
Rank-metric codes over arbitrary Galois extensions and rank analogues of Reed-Muller codes
Daniel Augot, Alain Couvreur, Julien Lavauzelle +1
This paper extends the study of rank-metric codes in extension fields equipped with an arbitrary Galois group . We propose a f…
A geometric characterization of minimal codes and their asymptotic performance
Gianira Nicoletta Alfarano, Martino Borello, Alessandro Neri
In this paper, we give a geometric characterization of minimal linear codes. In particular, we relate minimal linear codes to cutting blocking sets, introduced in a recent paper by…
Equivalence and Characterizations of Linear Rank-Metric Codes Based on Invariants
Alessandro Neri, Sven Puchinger, Anna-Lena Horlemann-Trautmann
We show that the sequence of dimensions of the linear spaces, generated by a given rank-metric code together with itself under several applications of a field automorphism, is an i…
Invariants and Inequivalence of Linear Rank-Metric Codes
Alessandro Neri, Sven Puchinger, Anna-Lena Horlemann-Trautmann
We show that the sequence of dimensions of the linear spaces, generated by a given rank-metric code together with itself under several applications of a field automorphism, is an i…
Tensor Representation of Rank-Metric Codes
Eimear Byrne, Alessandro Neri, Alberto Ravagnani +1
We present the theory of rank-metric codes with respect to the 3-tensors that generate them. We define the generator tensor and the parity check tensor of a matrix code, and descri…