Vortrag
eSeminar: Bounds on List Decoding of Linearized Reed-Solomon Codes
Vortrag von Dr. Sven Puchinger
Datum: 26.05.21 Zeit: 15.00 - 16.00 Raum:
(**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 **)
Linearized Reed-Solomon (LRS) codes are sum-rank-metric codes
that fulfill the Singleton bound with equality. In the two extreme cases
of the sum-rank metric, they coincide with Reed–Solomon codes (Hamming
metric) and Gabidulin codes (rank metric). List decoding in these
extreme cases is well-studied, and the two code classes behave very
differently in terms of list size, but nothing is known for the general
case. In this talk, we derive a lower bound on the list size for LRS
codes, which is, for a large class of LRS codes, exponential directly
above the Johnson radius. Furthermore, we show that some families of
linearized Reed–Solomon codes with constant numbers of blocks cannot be
list decoded beyond the unique decoding radius. The results are joint
work with Johan Rosenkilde.