Latroids and code invariants

Latroids were introduced by Vertigan, who associated a latroid to a linear block code and showed that its Tutte polynomial determines the weight enumerator of the code. We associate a latroid to a code over a ring or a field endowed with a general support function, and show that the generalized weights of the code can be recovered from the associated latroid. This provides a uniform framework for studying generalized weights of linear block codes, linear codes over a ring, rank-metric and sum-rank metric codes. Under suitable assumptions, we show that the latroid determines the weight distribution of the code.