Frame Stabilizers for Framed Vertex Operator Algebras Associated to Lattices Having 4-Frames

In this paper, we study certain Virasoro frames for lattice vertex operator algebras (VOAs) and their $\mathbb Z_2$-orbifolds using linear codes over $\mathbb Z_4$. We also compute the corresponding frame stabilizer from the viewpoint of binary codes and $\mathbb Z_4$-codes. As an application, we determine the frame stabilizers of several Virasoro frames of the VOA ${\mathrm VOA}\ V_{E_8}$ and the moonshine vertex operator algebra V^♮.