  We present a precise characterization of linear functional-repair storage
codes in terms of {\em admissible states/}, with each state made up from a
collection of vector spaces over some fixed finite field. To illustrate the
usefulness of our characterization, we provide several applications. We first
describe a simple construction of functional-repair storage codes for a family
of code parameters meeting the cutset bound outside the MBR and MSR points;
these codes are conjectured to have optimal rate with respect to their repair
locality. Then, we employ our characterization to develop a construction method
to obtain functional repair codes for given parameters using symmetry groups,
which can be used both to find new codes and to improve known ones. As an
example of the latter use, we describe a beautiful functional-repair storage
code that was found by this method, with parameters belonging to the family
investigated earlier, which can be specified in terms of only eight different
vector spaces.
