The geometry of covering codes in the sum-rank metric

Matteo Bonini; Martino Borello; Eimear Byrne

doi:10.48550/arXiv.2410.12393

The geometry of covering codes in the sum-rank metric

Matteo Bonini
, Martino Borello
, Eimear Byrne

Research output: Working paper/Preprint › Preprint

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Abstract

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-$\rho$-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.

Original language	English
Publisher	arXiv
Number of pages	12
DOIs	https://doi.org/10.48550/arXiv.2410.12393
Publication status	Published - 16 Oct 2024

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title = "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 a covering properties of a sum-rank metric code. We consider the problem of determining the shortest sum-rank-\$\textbackslash{}rho\$-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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The geometry of covering codes in the sum-rank metric

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