Seminar on Coding Theory
Date and time:: Thursday, 12th January 2023 at 2.30 pm
Venue: Ramanujan Hall
Speaker: Mahir Bilen Can
Affiliation: Tulane University, New Orleans, USA
Host: Sudhir Ghorpade
Title: Dual Higher Grassman Codes
Abstract: The Grassmann variety of k-dimensional subspaces of an n-dimensional vector space over a finite field with q-elements can be thought of as the ``moduli space'' of all linear q-ary (n,k)-codes. At the same time, each Grassmann variety naturally provides an algebraic geometry code via its Plucker embedding. The structure of Grassmann codes has been parsed by many researchers, most notably by Ghorpade. In this talk, we will discuss a fruitful generalization of the Grassmann codes by using the embeddings of Grassmannians into higher dimensional projective spaces. This new family of ``higher Grassmann codes'' has interesting connections with representation theory of SL_n over finite fields.