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We give a lattice theoretical interpretation of generalized deep holes of theLeech lattice VOA $V_\Lambda$. We show that a generalized deep hole defines a"true" automorphism invariant deep hole of the Leech lattice. We also show thatthere is a correspondence between the set of isomorphism classes of holomorphicVOA $V$ of central charge $24$ having non-abelian $V_1$ and the set ofequivalence classes of pairs $(\tau, \tilde{\beta})$ satisfying certainconditions, where $\tau\in Co_0$ and $\tilde{\beta}$ is a $\tau$-invariant deephole of squared length $2$. It provides a new combinatorial approach towardsthe classification of holomorphic VOAs of central charge $24$. In particular,we give an explanation for an observation of G. H\"ohn, which relates theweight one Lie algebras of holomorphic VOAs of central charge $24$ to certaincodewords associated with the glue codes of Niemeier lattices.

A lattice theoretical interpretation of generalized deep holes of the Leech lattice vertex operator algebra