Year: 2025
Type: article
Abstract: We introduce the concept of a sum–rank saturating system and outline its correspondence to covering properties of a sum–rank metric code. We consider the problem of determining the shortest length of a sum–rank- $$\rho $$ ρ -saturating system of a fixed dimension, which is equivalent to the covering problem in the sum–rank metric. We obtain upper and lower bounds on this quantity. We also give constructions of saturating systems arising from geometrical structures.
Source: Designs Codes and Cryptography
Authors: Matteo Bonini, Martino Borello, Eimear Byrne
Institutions: Aalborg University, Centre National de la Recherche Scientifique, Institut national de recherche en sciences et technologies du numérique, Université Sorbonne Paris Nord, Laboratoire Analyse, Géométrie et Applications, Centre Inria de Saclay, Laboratoire d'Informatique de l'École Polytechnique, GRACE: Geometry, arithmetic, algorithms, codes and encryption, Université Paris 8, University College Dublin
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4403578077