Fundamental Properties of Sum-Rank-Metric Codes

Eimear Byrne, Heide Gluesing-Luerssen, Alberto Ravagnani

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

This paper investigates the theory of sum-rank-metric codes for which the individual matrix blocks may have different sizes. Various bounds on the cardinality of a code are derived, along with their asymptotic extensions. The duality theory of sum-rank-metric codes is also explored, showing that MSRD codes (the sum-rank analogue of MDS codes) dualize to MSRD codes only if all matrix blocks have the same number of columns. In the latter case, duality considerations lead to an upper bound on the number of blocks for MSRD codes. The paper also contains various constructions of sum-rank-metric codes for variable block sizes, illustrating the possible behaviours of these objects with respect to bounds, existence, and duality properties.

Original languageEnglish
Pages (from-to)6456-6475
Number of pages20
JournalIEEE Transactions on Information Theory
Volume67
Issue number10
DOIs
StatePublished - Oct 2021

Bibliographical note

Publisher Copyright:
© 1963-2012 IEEE.

Keywords

  • MSRD code
  • MacWilliams identity
  • Sum-rank-metric code
  • asymptotic bound
  • bound
  • code construction
  • duality

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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