Integer sequences that are generalized weights of a linear code

Generalized weights are a well-studied family of invariants, originally defined for linear block codes in 1977. Their importance stems from the fact that they characterize the code robustness against wiretapping. After a short introduction to the topic, in this talk we will investigate which sequences of integers can be the generalized weights of various types of error-correcting codes: linear block codes, rank-metric codes, and the more general case of sum-rank metric codes.