6 papers
The multilinear forms Cayley graph and the eigenvalue method for tensor codes
Eimear Byrne, Lucien François
The connections between graph theory, and more generally association schemes, and coding theory were established by Delsarte for the Hamming metric and rank-metric codes. The ambie…
Constructions of Rank-Metric Codes of Small Tensor Rank
Matteo Bonini, Eimear Byrne, Giuseppe Cotardo
Rank-metric codes are subspaces of matrices over finite fields endowed with the rank metric and admit a natural tensorial representation. The tensor rank provides a measure of the…
Decoding Algorithms for Tensor Codes
Eimear Byrne, Alain Couvreur, Lucien François
Tensor codes are a generalisation of matrix codes. Such codes are defined as subspaces of order-r tensors for which the ambient space is endowed with the tensor-rank as a metric. A…
q-Polymatroids associated with restricted rank-metric codes
Eimear Byrne, Giovanni Longobardi, and Rocco Trombetti
In this article, we study polymatroids that are representable by means of linear restricted rank-metric codes, namely, by subspaces of the space of alternating, symmetric, or Hermi…
A -Polymatroid Framework for Information Leakage in Secure Linear Network Coding
Eimear Byrne, Johan Vester Dinesen, Ragnar Freij-Hollanti +1
We study information leakage in secure linear network coding schemes based on nested rank-metric codes. We show that the amount of information leaked to an adversary that observes…
Secret Sharing in the Rank Metric
Johan Vester Dinesen, Eimear Byrne, Ragnar Freij-Hollanti +1
The connection between secret sharing and matroid theory is well established. In this paper, we generalize the concepts of secret sharing and matroid ports to -polymatroids. Spe…