Vortrag
Codes with extremality properties in the rank metric
Vortrag von Cristina Landolina
Datum: 16.02.22 Zeit: 15.00 - 16.00 Raum:
Codes in the rank metric were first discovered 1978 by Delsarte. These
codes have attracted attention lately due to their considerabile list of
applications. A rank-metric code can be considered as an F_q-linear
space of n times m matrices over the finite field of q elements. Several
bounds relating the parameters of a rank-metric code can be derived. We
will discuss the Anticode bound relating the dimension of a code with
its maximum rank. To this end we will present the classification of
Optimal Anticodes, which are codes attaining this bound. A new, more
general Anticode bound is presented. We will study and completely
classify a larger family of rank-metric codes attaining this new bound.
This codes are called (dually) quasi Optimal Anticodes. Moreover we will
show how invariants such as the generalized weights and the rank
distribution of (dually) quasi Optimal Anticodes can be easily derived
from the structural classification of the latter.
(**Please note that a 2G certificate is mandatory for in-person attendance.**)
(**This eSeminar will also be live-streamed on Zoom, using the same meeting details as previous seminars. If you do not have meeting details, please contact simran.tinani@math.uzh.ch **)