Monday, July 12, 3pm ET (8pm BST, 7am Tue NZST)
Eimear Byrne, University College Dublin
Some recent results on q-matroids
The q-analogue of a (poly)matroid has been a topic of recent interest among the coding theory community, due to their connections with rank-metric codes (see e.g. [GJLR20], [JP18], [Shi19]). When defining a q-(poly)matroid, we associate a rank function with the lattice of subspaces of a finite dimensional space E. As one might expect, there are several cryptomorphic descriptions of a q-matroid, in terms of independent spaces, circuits, flats, etc. We will go through some of these, highlighting the difference to the classical case. We will also outline some applications of q-(poly)matroids to the construction of the q-analogue of a t-design.