Monday, July 12, 3pm ET (8pm BST, 7am Tue NZST)
Eimear Byrne, University College Dublin
Some recent results on q-matroids

Abstract:
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.

Some of the results of this talk are based on joint work with Michela Ceria, Sorina Ionica, Relinde Jurrius and Elif Sacikara.

[JP18] Relinde Jurrius and Ruud Pellikaan. Defining the q-analogue of a matroid. Electronic Journal of Combinatorics, 25(3):P3.2, 2018.

[GJLR20] Elisa Gorla, Relinde Jurrius, Hiram H L´opez, and Alberto Ravagnani. Rank-metric codes and q-polymatroids. Journal of Algebraic Combinatorics, 52:1–19, 2020.

[Shi19] Keisuke Shiromoto. Codes with the rank metric and matroids. Designs, Codes and Cryptography, 87(8):1765–1776, 2019.