Anticodes in the sum-rank metric

Eimear Byrne; Heide Gluesing-Luerssen; Alberto Ravagnani

doi:10.1016/j.laa.2022.02.012

Anticodes in the sum-rank metric

Eimear Byrne, Heide Gluesing-Luerssen, Alberto Ravagnani

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We study the structure of anticodes in the sum-rank metric for arbitrary fields and matrix blocks of arbitrary sizes. Our main result is a complete classification of optimal linear anticodes. We also compare the cardinality of the ball in the sum-rank metric with that of an optimal linear anticode, showing that the latter is strictly larger over sufficiently large finite fields. Finally, we give examples of parameters for which the largest anticode is neither a ball nor a linear anticode.

Original language	English
Pages (from-to)	80-98
Number of pages	19
Journal	Linear Algebra and Its Applications
Volume	643
DOIs	https://doi.org/10.1016/j.laa.2022.02.012
State	Published - Jun 15 2022

Bibliographical note

Publisher Copyright:
© 2022 The Author(s)

Funding

H. Gluesing-Luerssen was partially supported by the grant #422479 from the Simons Foundation.A. Ravagnani is partially supported by the Dutch Research Council through grant VI.Vidi.203.045.

Funders	Funder number
Simons Foundation
Nederlandse Organisatie voor Wetenschappelijk Onderzoek	VI.Vidi.203.045

Keywords

Anticode
Matrix code
Sum-rank metric

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/j.laa.2022.02.012

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abstract = "We study the structure of anticodes in the sum-rank metric for arbitrary fields and matrix blocks of arbitrary sizes. Our main result is a complete classification of optimal linear anticodes. We also compare the cardinality of the ball in the sum-rank metric with that of an optimal linear anticode, showing that the latter is strictly larger over sufficiently large finite fields. Finally, we give examples of parameters for which the largest anticode is neither a ball nor a linear anticode.",

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AU - Gluesing-Luerssen, Heide

AU - Ravagnani, Alberto

PY - 2022/6/15

Y1 - 2022/6/15

N2 - We study the structure of anticodes in the sum-rank metric for arbitrary fields and matrix blocks of arbitrary sizes. Our main result is a complete classification of optimal linear anticodes. We also compare the cardinality of the ball in the sum-rank metric with that of an optimal linear anticode, showing that the latter is strictly larger over sufficiently large finite fields. Finally, we give examples of parameters for which the largest anticode is neither a ball nor a linear anticode.

AB - We study the structure of anticodes in the sum-rank metric for arbitrary fields and matrix blocks of arbitrary sizes. Our main result is a complete classification of optimal linear anticodes. We also compare the cardinality of the ball in the sum-rank metric with that of an optimal linear anticode, showing that the latter is strictly larger over sufficiently large finite fields. Finally, we give examples of parameters for which the largest anticode is neither a ball nor a linear anticode.

KW - Anticode

KW - Matrix code

KW - Sum-rank metric

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VL - 643

SP - 80

EP - 98

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Anticodes in the sum-rank metric

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

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