Projective metrics were first introduced by Gabidulin and Simonis in 1997 as a generalization of some already well-studied metrics like the Hamming metric, rank-metric, sum-rank metric, burst metrics and combinatorial metrics. Several other metrics were later also studied in this context, e.g. the rank-metric supported on Ferrers diagrams, the term-rank or cover metric, the phase rotation metric, and metrics based on BCH codes or GRS codes. 

Projective metrics form a large class of translation-invariant metrics on vector spaces and contain many metrics of interest for coding theory. In this talk we will go through the fundamentals of the theory and show how some classic coding-theory results, e.g. a Singleton-like bound, at the moment separately proven for a few of these metrics, can be derived in general for all projective metrics, including those yet to be researched. 

This is joint work with Gabor Riccardi.