**Date & Time:** Thursday, August 13, 2015, 17:30-18:30.

**Venue:** Room 113

**Title:** A systematic local encoder for Grassmann codes and related codes

**Speaker:** Fernando Pinero, IIT Bombay

**Abstract:** We introduce the concept of an iterative encoder, which uses a
short, simple code with a deletion decoder and an incidence structure to
define and encode a Tanner code. Previously we discussed the structure of
the parity check equations of Grassmann codes and showed how these relate
to the lines of the Grassmannian in the algebraic, geometric and
combinatorial way. We also proved that the Grassmann code is a Tanner code
of its point line incidence graph and the simplest Grassmann code.
We will prove that by taking the lines of the Grassmannian and a special
subset of the Grassmannian, called an apartment, we can encode the parity
check bits of the Grassmannian locally and without the need of iteration.
We will further prove that this encoder also works for Schubert union codes
and, if time permits, for affine Grassmann codes. Furthermore, this
encoding algorithm gives also an alternative proof of the fact that the
dual Grassmann code or the related code is generated by its parity check
bits.