The theory of shellable simplicial complexes brings together combinatorics, algebra, and topology in a remarkable way. It is a classical result that matroid complexes, that is, simplicial complexes formed by the class of independent subsets in a matroid, are shellable. This has some bearing on the study of linear block codes, especially in regard to their Betti numbers and generalized weight enumerator polynomials. 

We now know that q-matroids have close connections with rank metric codes in a manner similar to the connection between matroids and codes. A recent result establishes shellability of q-matroid complexes and also determines the homology of these complexes in many cases. The determination of homology has now been completed for arbitrary q-matroid complexes. 

We will outline these developments whlie making an attempt to keep the prerequisites at a minimum. 

The contents of this talk are based on a joint work with Rakhi Pratihar and Tovohery Randrianarisoa, and also with Rakhi Pratihar, Tovohery Randrianarisoa, Hugues Verdure and Glen Wilson.