AUTOMORPHISM GROUPS AND ISOMETRIES FOR CYCLIC ORBIT CODES

Heide Gluesing-Luerssen, Hunter Lehmann

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We study orbit codes in the field extension Fq n . First we show that the automorphism group of a cyclic orbit code is contained in the normalizer of the Singer subgroup if the orbit is generated by a subspace that is not contained in a proper subfield of Fq n . We then generalize to orbits under the normalizer of the Singer subgroup. In that situation some exceptional cases arise and some open cases remain. Finally we characterize linear isometries between such codes.

Original languageEnglish
Pages (from-to)119-138
Number of pages20
JournalAdvances in Mathematics of Communications
Volume17
Issue number1
DOIs
StatePublished - 2023

Bibliographical note

Publisher Copyright:
© 2023, American Institute of Mathematical Sciences. All rights reserved.

Keywords

  • Singer cycles
  • Subspace codes
  • automorphism groups
  • cyclic orbit codes
  • field-extension subgroups
  • linear isometries

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computer Networks and Communications
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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