Three dimensional topological superconductors with time reversal symmetry (class DIII) are indexed by an integer
ν, the number of surface Majorana cones, according to the free fermion classification. The superfluid B phase of He
3 realizes the
ν=1 phase. Recently, it has been argued that this classification is reduced in the presence of interactions to Z
16. This was argued from the symmetry respecting surface topological orders of these states, which provide a non-perturbative definition of the bulk topological phase. Here, we verify this conclusion by focusing on the even index case,
ν=2m, where a vortex condensation approach can be used to explicitly derive the surface topological orders. We show a direct relation to the well known result on one dimensional topological superconductors (class BDI), where interactions reduce the free fermion classification from Z down to Z
8. Finally, we discuss in detail the fermionic analog of Kramers time reversal symmetry, which allows semions of some surface topological orders to transform as
T2=±i.
We show that interactions can drive a class of higher order topological superconductors (HOTSCs) into symmetry-enriched topologically ordered phases exemplified by topological quantum error correcting codes. In two dimensions, interacting HOTSCs realize various topologically ordered surface and color codes. In three dimensions, interactions can drive HOTSCs protected by subsystem symmetries into recently discovered fracton phases. We explicitly relate fermion parity operators underlying the gapless excitations of the HOTSC to the Wilson algebra of symmetry-enriched quantum codes. Arrays of crossed Majorana wires provide an experimental platform for realizing fracton matter and for probing the quantum phase transition between HOTSCs and the topologically ordered phase.