The automorphism group of the Hamming code vertex operator algebra (Q1570875)

The code vertex operator algebra \(V_D\) associated to an even binary linear code \(D\) is a sum of tensor products of the Ising model, the irreducible unitary highest weight representations of the Virasoro algebra of central charge \(1/2\), where the number of the factors is the length of the code \(D\), and the summands are in one-to-one correspondence with \(D\) by forming the tensor product of \(L(1/2,0)\)'s and \(L(1/2, 1/2)\)'s according codewords. In this paper, the authors determine the automorphism group of \(V_D\) when \(D\) is the \([8,4,4]\) extended binary Hamming code, and establish an isomorphism of the group onto the trio stabilizer of the largest Mathieu group \(M_{24}\).