Title: Ferrers Diagram Rank-Metric Codes

Abstract: Our codes of interest are subspaces of $F_q^{m\times n}$ in which every nonzero matrix has rank at least $\delta$, and conforms to the shape of a given Ferrers diagram. In 2009, Etzion and Silberstein proved an upper bound for the dimension of such codes, and conjectured that it was achievable for any given parameters. In particular, the case for unrestricted matrices was solved in 1985 by Gabidulin, predating the complications brought on by nontrivial Ferrers diagram shapes. In this talk, we will prove the bound and discuss several known cases of the conjecture, including two new cases.