  The $[[7,1,3]]$ Steane code and $[[23,1,7]]$ quantum Golay code have been
identified as good candidates for fault-tolerant quantum computing via code
concatenation. These two codes have transversal implementations of all Clifford
gates, but require some other scheme for fault-tolerant $T$ gates. Using magic
states, Clifford operations, and measurements is one common scheme, but magic
state distillation can have a large overhead. Code conversion is one avenue for
implementing a universal gate set fault-tolerantly without the use of magic
state distillation. Analogously to how the $[[7,1,3]]$ Steane code can be
fault-tolerantly converted to and from the $[[15,1,3]]$ Reed-Muller code which
has a transversal $T$ gate, the $[[23,1,7]]$ Golay code can be converted to a
$[[95,1,7]]$ triorthogonal code with a transversal $T$ gate. A crucial
ingredient to this procedure is the $[[49,1,5]]$ triorthogonal code, which can
itself be seen as related to the self-dual $[[17,1,5]]$ 2D color code.
Additionally, a method for code conversion based on a transversal CNOT between
the codes, rather than stabilizer measurements, is described.
