The geometry of covering codes in the sum–rank metric

Matteo Bonini; Martino Borello; Eimear Byrne

doi:10.1007/s10623-025-01628-6

The geometry of covering codes in the sum–rank metric

Matteo Bonini^*, Martino Borello, Eimear Byrne

^*Corresponding author for this work

Research output: Contribution to journal › Journal article › Research › peer-review

Abstract

We introduce the concept of a sum–rank saturating system and outline its correspondence to covering properties of a sum–rank metric code. We consider the problem of determining the shortest length of a sum–rank-ρ-saturating system 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
Article number	105658
Journal	Designs, Codes, and Cryptography
ISSN	0925-1022
DOIs	https://doi.org/10.1007/s10623-025-01628-6
Publication status	Accepted/In press - 2025

Bibliographical note

Publisher Copyright:
© The Author(s) 2025.

Keywords

Covering radius
Linear sets
Saturating sets
Sum–rank metric codes

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10.1007/s10623-025-01628-6

Cite this

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AU - Borello, Martino

AU - Byrne, Eimear

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PY - 2025

Y1 - 2025

N2 - We introduce the concept of a sum–rank saturating system and outline its correspondence to covering properties of a sum–rank metric code. We consider the problem of determining the shortest length of a sum–rank-ρ-saturating system 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.

AB - We introduce the concept of a sum–rank saturating system and outline its correspondence to covering properties of a sum–rank metric code. We consider the problem of determining the shortest length of a sum–rank-ρ-saturating system 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.

KW - Covering radius

KW - Linear sets

KW - Saturating sets

KW - Sum–rank metric codes

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DO - 10.1007/s10623-025-01628-6

M3 - Journal article

AN - SCOPUS:105002164546

SN - 0925-1022

JO - Designs, Codes, and Cryptography

JF - Designs, Codes, and Cryptography

M1 - 105658

ER -

The geometry of covering codes in the sum–rank metric

Abstract

Bibliographical note

Keywords

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