Covering Properties of Sum-Rank Metric Codes

Cornelia Ott, Hedongliang Liu, Antonia Wachter-Zeh

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 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 languageEnglish
Title of host publication2022 58th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2022
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9798350399981
DOIs
StatePublished - 2022
Event58th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2022 - Monticello, United States
Duration: 27 Sep 202230 Sep 2022

Publication series

Name2022 58th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2022

Conference

Conference58th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2022
Country/TerritoryUnited States
CityMonticello
Period27/09/2230/09/22

Keywords

  • bounds
  • cardinality
  • covering radius
  • sum-rank metric codes

Fingerprint

Dive into the research topics of 'Covering Properties of Sum-Rank Metric Codes'. Together they form a unique fingerprint.

Cite this