  We consider the Radon transform along lines in an $n$ dimensional vector
space over the two element field. It is well known that this transform is
injective and highly overdetermined. We classify the minimal collections of
lines for which the restricted Radon transform is also injective. This is an
instance of I.M.~Gelfand's {\it admissibility problem}. The solution is in
stark contrast to the more uniform cases of the affine hyperplane transform and
the projective line transform, which are addressed in other papers,
\cite{Feld-G,Gr1}. The presentation here is intended to be widely accessible,
requiring minimum background.
