Modul: MAT076 Arbeitsgemeinschaft in Codierungstheorie und Kryptographie

## On Sparseness of MRD codes and Semifields

Prof. Dr. Heide Gluesing-Luerssen talk

**Date:** 25.09.19 **Time:** 15.00 - 16.00 **Room:**

In this talk I will discuss the proportion of MRD codes within the space of all rank-metric codes of the same dimension. More specifically, I will consider the asymptotic behavior of this proportion as the field size tends to infinity. It turns out that, for instance, [3x2;2]-MRD codes have an asymptotic proportion of 1/3. On the other hand, for [3x3;3]-MRD codes this asymptotic proportion is zero, and therefore we call this class of MRD codes sparse. The proof of the sparsity follows from a parametrization of 3-dimensional semifields by Menichetti (1973). I will discuss the relation between MRD codes and semifields and present the main steps of the proof.