  We initiate the study of Majorana fermion codes. These codes can be viewed as
extensions of Kitaev's 1D model of unpaired Majorana fermions in quantum wires
to higher spatial dimensions and interacting fermions. The purpose of Majorana
fermion codes (MFCs) is to protect quantum information against low-weight
fermionic errors, that is, operators acting on sufficiently small subsets of
fermionic modes. We examine to what extent MFCs can surpass qubit stabilizer
codes in terms of their stability properties. A general construction of 2D MFCs
is proposed which combines topological protection based on a macroscopic code
distance with protection based on fermionic parity conservation. Finally, we
use MFCs to show how to transform any qubit stabilizer code to a weakly
self-dual CSS code.
