Covering Properties of Sum-Rank Metric Codes

Cornelia Ott; Hedongliang Liu; Antonia Wachter-Zeh

doi:10.1109/Allerton49937.2022.9929421

Covering Properties of Sum-Rank Metric Codes

Cornelia Ott, Hedongliang Liu, Antonia Wachter-Zeh

Associate Professorship of Coding and Cryptography

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

5 Scopus citations

Abstract

The sum-rank metric can be seen as a generalization of both, the rank and the Hamming metric. It is well known that sum-rank metric codes outperform rank metric codes in terms of the required field size to construct maximum distance separable codes (i.e., the codes achieving the Singleton bound in the corresponding metric). In this work, we investigate the covering property of sum-rank metric codes to enrich the theory of sum-rank metric codes. We intend to answer the question: what is the minimum cardinality of a code given a sum-rank covering radius? We show the relations of this quantity between different metrics and provide several lower and upper bounds for sum-rank metric codes.

Original language	English
Title of host publication	2022 58th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2022
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)	9798350399981
DOIs	https://doi.org/10.1109/Allerton49937.2022.9929421
State	Published - 2022
Event	58th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2022 - Monticello, United States Duration: 27 Sep 2022 → 30 Sep 2022

Publication series

Name	2022 58th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2022

Conference

Conference	58th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2022
Country/Territory	United States
City	Monticello
Period	27/09/22 → 30/09/22

Keywords

bounds
cardinality
covering radius
sum-rank metric codes

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10.1109/Allerton49937.2022.9929421

Cite this

Ott, C., Liu, H., & Wachter-Zeh, A. (2022). Covering Properties of Sum-Rank Metric Codes. In 2022 58th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2022 (2022 58th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2022). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/Allerton49937.2022.9929421

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abstract = "The sum-rank metric can be seen as a generalization of both, the rank and the Hamming metric. It is well known that sum-rank metric codes outperform rank metric codes in terms of the required field size to construct maximum distance separable codes (i.e., the codes achieving the Singleton bound in the corresponding metric). In this work, we investigate the covering property of sum-rank metric codes to enrich the theory of sum-rank metric codes. We intend to answer the question: what is the minimum cardinality of a code given a sum-rank covering radius? We show the relations of this quantity between different metrics and provide several lower and upper bounds for sum-rank metric codes.",

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author = "Cornelia Ott and Hedongliang Liu and Antonia Wachter-Zeh",

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language = "English",

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Ott, C, Liu, H & Wachter-Zeh, A 2022, Covering Properties of Sum-Rank Metric Codes. in 2022 58th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2022. 2022 58th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2022, Institute of Electrical and Electronics Engineers Inc., 58th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2022, Monticello, United States, 27/09/22. https://doi.org/10.1109/Allerton49937.2022.9929421

Covering Properties of Sum-Rank Metric Codes. / Ott, Cornelia; Liu, Hedongliang; Wachter-Zeh, Antonia.
2022 58th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2022. Institute of Electrical and Electronics Engineers Inc., 2022. (2022 58th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2022).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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T1 - Covering Properties of Sum-Rank Metric Codes

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AU - Liu, Hedongliang

AU - Wachter-Zeh, Antonia

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N2 - The sum-rank metric can be seen as a generalization of both, the rank and the Hamming metric. It is well known that sum-rank metric codes outperform rank metric codes in terms of the required field size to construct maximum distance separable codes (i.e., the codes achieving the Singleton bound in the corresponding metric). In this work, we investigate the covering property of sum-rank metric codes to enrich the theory of sum-rank metric codes. We intend to answer the question: what is the minimum cardinality of a code given a sum-rank covering radius? We show the relations of this quantity between different metrics and provide several lower and upper bounds for sum-rank metric codes.

AB - The sum-rank metric can be seen as a generalization of both, the rank and the Hamming metric. It is well known that sum-rank metric codes outperform rank metric codes in terms of the required field size to construct maximum distance separable codes (i.e., the codes achieving the Singleton bound in the corresponding metric). In this work, we investigate the covering property of sum-rank metric codes to enrich the theory of sum-rank metric codes. We intend to answer the question: what is the minimum cardinality of a code given a sum-rank covering radius? We show the relations of this quantity between different metrics and provide several lower and upper bounds for sum-rank metric codes.

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Covering Properties of Sum-Rank Metric Codes

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