  In 2004, Ehrenfeucht, Harju, and Rozenberg showed that any graph on a vertex
set $V$ can be obtained from a complete graph on $V$ via a sequence of the
operations of complementation, switching edges and non-edges at a vertex, and
local complementation. The last operation involves taking the complement in the
neighbourhood of a vertex. In this paper, we consider natural generalizations
of these operations for binary matroids and explore their behaviour. We
characterize all binary matroids obtainable from the binary projective geometry
of rank $r$ under the operations of complementation and switching. Moreover, we
show that not all binary matroids of rank at most $r$ can be obtained from a
projective geometry of rank $r$ via a sequence of the three generalized
operations. We introduce a fourth operation and show that, with this additional
operation, we are able to obtain all binary matroids.
