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 language | English |
|---|---|
| Pages (from-to) | 119-138 |
| Number of pages | 20 |
| Journal | Advances in Mathematics of Communications |
| Volume | 17 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2023 |
Bibliographical note
Funding Information:2020 Mathematics Subject Classification. Primary: 94B60. Key words and phrases. Subspace codes, automorphism groups, linear isometries, cyclic orbit codes, field-extension subgroups, Singer cycles. The first author was partially supported by the grant #422479 from the Simons Foundation. ∗ Corresponding author: Heide-Gluesing Luerssen.
Publisher Copyright:
© 2023, American Institute of Mathematical Sciences. All rights reserved.
Keywords
- automorphism groups
- cyclic orbit codes
- field-extension subgroups
- linear isometries
- Singer cycles
- Subspace codes
ASJC Scopus subject areas
- Algebra and Number Theory
- Computer Networks and Communications
- Discrete Mathematics and Combinatorics
- Applied Mathematics