Zusammenfassung für den Vortrag am 20.04.2022 (14:00 Uhr)

Seminar on Nonlinear Algebra

Gianira Nicoletta Alfarano (University of Zurich)
q-Analogues of Matroids and Codes

In classical combinatorics, matroids generalize the notion of linear independence of vectors over a field. In this talk, we will introduce the concept of \(\mathbb F_{q^m}\)-independence of \(\mathbb F_q\)-spaces and we show that \(q\)-matroids generalize this notion. As a consequence, the independent spaces of a representable \(q\)-matroid will be defined as the \(\mathbb F_{q^m}\)-independent subspaces of the \(q\)-system associated to an \(\mathbb F_{q^m}\)-linear rank-metric code. Moreover, we will further investigate the link between codes and matroids.