Constructions of the moonshine vertex operator algebra by using orbifold theories

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By this research project, we obtain a new construction of the moonshine vertex operator algebra based on quadratic spaces. As an application, we obtain a new description of a maximal subgroup of the Monster simple group. This is an analog of the known constructions of the Golay code and Leech lattice. Hence we obtain a new relation among codes, lattices and vertex operator algebras. Moreover, by this approach, we would construct new holomorphic vertex operator algebras of central charge 24.