Pré-Publication, Document De Travail Année : 2024

The geometry of covering codes in the sum-rank metric

Résumé

We introduce the concept of a sum-rank saturating system and outline its correspondence to a covering properties of a sum-rank metric code. We consider the problem of determining the shortest sum-rank-ρ-saturating systems 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.
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Dates et versions

hal-04897367 , version 1 (20-01-2025)

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  • HAL Id : hal-04897367 , version 1

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Matteo Bonini, Martino Borello, Eimear Byrne. The geometry of covering codes in the sum-rank metric. 2024. ⟨hal-04897367⟩
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