The geometry of covering codes in the sum–rank metric
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- $$\rho $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ρ</mml:mi> </mml:math> -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.
Authors
- Martino Borello (ORCID: https://orcid.org/0000-0002-4597-1244)
- Matteo Bonini (ORCID: https://orcid.org/0000-0001-9326-1370)
- Eimear Byrne (ORCID: https://orcid.org/0000-0002-1857-0365)
Institutions
- University College Dublin (IE)
- Centre National de la Recherche Scientifique (FR)
- Institut national de recherche en sciences et technologies du numérique (FR)
- École Polytechnique (FR)
- Sorbonne Université (FR)
- Université Sorbonne Paris Nord (FR)
- Laboratoire Analyse, Géométrie et Applications (FR)
- Centre Inria de Saclay (FR)
- Université Paris 8 (FR)
- Aalborg University (DK)
Publication Details
- Journal
- Designs Codes and Cryptography
- Published
- 2025-04-09
- DOI
- https://doi.org/10.1007/s10623-025-01628-6
- Primary Topic
- Coding theory and cryptography
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Agence Nationale de la Recherche
- Aalborg Universitet