Talk
Bounds and optimal codes in the Lee metric
Talk by Dr. Violetta Weger
Date: 11.05.22 Time: 15.00 - 16.00 Room:
Coding theory traditionally deals with subspaces over finite fields endowed with the Hamming metric and the study of optimal codes (with regard to some bounds) plays a key role. In particular, codes that achieve the Singleton bound, namely MDS codes, are well-studied. We know that being an MDS code is invariant under duality and furthermore, being MDS is a generic property, meaning that the probability of a random code being MDS tends to 1 as we let the field size grow.
In this talk we will slightly move away from the classical setting and consider similar questions for integer residue rings endowed with the Lee metric.
For this we first investigate the Singleton bound in the Lee metric, where we will see that maximum Lee distance codes are extremely sparse. Due to this result, we then change our focus to the Plotkin bound, where we will improve the known bound and close a gap in the characterization of their optimal codes, namely constant Lee weight codes.
Since this research area is still full of open questions, we also hope to encourage its further research by providing helpful tools and insights.
This talk is based on a joint work with Eimear Byrne.
(**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 **)