Abstract :
We study the representation theory of code vertex operator algebrasMD(VOAs) constructed from an even binary linear codeD. Our main purpose is to study, using the representation theory ofMD, the structure of VOAVcontaining a set of mutually orthogonal rational conformal vectors with central charge such that the sum of them is the Virasoro element ofV. The most famous example of such VOAs is the Moonshine VOAV . If a simple VOAVcontains such a set of conformal vectors, thenVhas an elementary Abelian automorphism 2-groupPgenerated by involutions. As aP-module,Vhas a decompositionV = χ Irr(P)Vχas the direct sum of weight spacesVχofP. It was proved thatVχis an irreducibleVP-module. Therefore, we can expect that the classification of irreducibleVP-modules and their fusion rules will determine the structure ofV. We will show that the fixed point spaceVPis isomorphic to a code VOAMDof some binary linear even codeD, and then study and classify all irreducibleMD-modules and compute the fusion rules of some of them.
