Modul: MAT076 Arbeitsgemeinschaft in Codierungstheorie und Kryptographie

## eSeminar: Automorphisms of Cyclic Orbit Codes

Talk by Hunter Lehmann

**Date:** 21.04.21 **Time:** 15.00 - 16.00 **Room:**

(**This eSeminar will take place on Zoom, using the same meeting details as previous seminars. If you do not have meeting details, please contact simran.tinani@math.uzh.ch **)

Cyclic orbit codes are a prominent class of subspace codes, generated by taking the orbit of a single subspace of the finite field $F_{q^n}$ under an action of a Singer subgroup. We are interested in classifying the isometry classes of these codes for various parameters. In order to do this, we show that the automorphism group of a cyclic orbit code is heavily related to the smallest subfield of the ambient field which contains a generating subspace for the code. When there is no proper subgroup of the ambient field containing a generator for the code, we see that any possible isometry is an element of the normalizer of the Singer subgroup.