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arXiv · 2410.12393

The geometry of covering codes in the sum-rank metric

Matteo Bonini·Martino Borello·Eimear Byrne
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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-$ρ$-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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Matteo Bonini, Martino Borello, Eimear Byrne. 2025-04-09. The geometry of covering codes in the sum-rank metric. https://arxiv.org/abs/2410.12393

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