Date & Time: Thursday, July 24, 2008, 15:00-16:00.
Venue: Ramanujan Hall
Title: Weight Hierarchy and Generalized Spectrum of Linear Codes Associated to Grassmann Varieties
Speaker: Arunkumar R. Patil, IIT Bombay
Abstract: We consider a class of linear error correcting codes associated to Grassmann varieties over finite fields with its canonical Plucker embedding. These are known as Grassmann codes, and some of their basic parameters, such as the dimension and the minimum distance, are known. In this thesis we develop new methods to recover most of the known results and also prove a number of new results concerning the higher weights and the generalized spectrum of Grassmann codes. This includes the determination of the complete weight hierarchy in the case of codes associated to the Grassmannian of 2-dimensional subspaces of an m-dimensional vector space. In the general case we give a conjectural description for the higher weights via a combinatorial object called a "subclose family". We also make a beginning in the more general problem of determining the generalized spectrum of Grassmann codes in a certain special case.