  It is known that there are 48 Virasoro algebras acting on the monster
conformal field theory. We call conformal field theories with such a property,
which are not necessarily chiral, code conformal field theories. In this paper,
we introduce a notion of a framed algebra, which is a finite-dimensional
non-associative algebra, and showed that the category of framed algebras and
the category of code conformal field theories are equivalent. We have also
constructed a new family of integrable conformal field theories using this
equivalence. These conformal field theories are expected to be useful for the
study of moduli spaces of conformal field theories.
