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

^*Kontaktforfatter

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › 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.

Originalsprog	Engelsk
Artikelnummer	105658
Tidsskrift	Designs, Codes, and Cryptography
ISSN	0925-1022
DOI	https://doi.org/10.1007/s10623-025-01628-6
Status	Accepteret/In press - 2025

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Publisher Copyright:
© The Author(s) 2025.

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10.1007/s10623-025-01628-6

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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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U2 - 10.1007/s10623-025-01628-6

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

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