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

Publikation: 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.

Originalsprog	Engelsk
Udgiver	arXiv
Antal sider	12
DOI	https://doi.org/10.48550/arXiv.2410.12393
Status	Udgivet - 16 okt. 2024

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math.CO
cs.IT
math.IT
05B40, 11T71, 51E20, 52C17, 94B75

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10.48550/arXiv.2410.12393

2410.12393v1Forlagets udgivne version, 224 KB

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The geometry of covering codes in the sum-rank metric

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