Representability of matroids by c-arrangements is undecidable

For a natural number c, c-arrangement is an arrangement of dimension c subspaces satisfying the following condition: sum any subset has multiple c. Matroids arising as normalized rank functions c-arrangements are also known multilinear matroids. We prove that it algorithmically undecidable whether there exists such given matroid representation, or equivalently multilinear. It follows certain problems on network coding and secret sharing schemes undecidable. In proof, we encode group presentations in frame matroids three which call generalized Dowling geometries: construction inspired by geometries finite groups von Staudt construction. The idea to construct reduction from uniform word problem for representability condition gives rise some difficulties their resolution main part paper.