Construction of Holomorphic Local Conformal Framed Nets

We construct holomorphic local conformal framed nets extended from a tensor power of the Virasoro net with $c=\frac {1}{2}$ with a pair of binary codes (C,D) satisfying the conditions given by Lam and Yamauchi for holomorphic framed vertex operator algebras. Our result is an operator algebraic counterpart of theirs, but our proof is entirely different. We apply the α-induction in order to identify the representation theory of “code local conformal net” and this gives rise to the existence of the desired local conformal net.