eSeminar: Automorphisms of Cyclic Orbit Codes

Vortrag von Hunter Lehmann

Datum: 21.04.21  Zeit: 15.00 - 16.00  Raum:

<a href="https://uzh.mediaspace.cast.switch.ch/media/eSeminar%3A%20Automorphisms%20of%20Cyclic%20Orbit%20Codes/0_p8uzvb1r/11634" target="_blank"><button>Video<i class="fa fa-play-circle"></i></button></a> (**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 **)<br><br> 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.