Anticodes in the sum-rank metric

Eimear Byrne, Heide Gluesing-Luerssen, Alberto Ravagnani

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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 languageEnglish
Pages (from-to)80-98
Number of pages19
JournalLinear Algebra and Its Applications
StatePublished - Jun 15 2022

Bibliographical note

Funding Information:
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.

Publisher Copyright:
© 2022 The Author(s)


  • 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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