We observe that every self-dual ternary code determines a holomorphic N=1
superconformal field theory. This provides ternary constructions of some
well-known holomorphic N=1 SCFTs, including Duncan's "supermoonshine" model and
the fermionic "beauty and the beast" model of Dixon, Ginsparg, and Harvey.
Along the way, we clarify some issues related to orbifolds of fermionic
holomorphic CFTs. We give a simple coding-theoretic description of the
supersymmetric index and conjecture that for every self-dual ternary code this
index is divisible by 24; we are able to prove this conjecture except in the
case when the code has length 12 mod 24. Lastly, we discuss a conjecture of
Stolz and Teichner relating N=1 SCFTs with Topological Modular Forms. This
conjecture implies constraints on the supersymmetric indexes of arbitrary
holomorphic SCFTs, and suggests (but does not require) that there should be,
for each k, a holomorphic N=1 SCFT of central charge 12k and index
24/gcd(k,24). We give ternary code constructions of SCFTs realizing this
suggestion for k \leq 5.