Details

Autor(en) / Beteiligte

• Bonini, Matteo
• Borello, Martino
• Byrne, Eimear

Titel

Saturating systems and the rank-metric covering radius

Ist Teil von

• Journal of algebraic combinatorics, 2023-12, Vol.58 (4), p.1173-1202

Ort / Verlag

New York: Springer US

Erscheinungsjahr

2023

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• We introduce the concept of a rank-saturating system and outline its correspondence to a rank-metric code with a given covering radius. We consider the problem of finding the value of s q m / q ( k , ρ ) , which is the minimum F q -dimension of a q -system in F q m k that is rank- ρ -saturating. This is equivalent to the covering problem in the rank metric. We obtain upper and lower bounds on s q m / q ( k , ρ ) and evaluate it for certain values of k and ρ . We give constructions of rank- ρ -saturating systems suggested from geometry.