So far, we have only seen codes coming from curves. More generally we can construct codes from higher dimensional varieties. Determining their basic parameters is a hard problem that leads to interesting questions in combinatorics and algebraic geometry. I will focus on codes defined by the Grassmannian and show how the study of Schubert cycles can help us determining some of those parameters.
The talk will be self contained. I will not assume any prior knowledge on Schubert varieties.