The automorphism group of the Hamming code vertex operator algebra
type: Item
instance of: scholarly article
title: The automorphism group of the Hamming code vertex operator algebra
zbMATH Open document ID: 0978.17023
author: Atsushi Matsuo
author: Mika Matsuo
published in: Journal of Algebra
publication date: 2002-02-12T00:00:00Z
review text: 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 \(M_{24}\).
Mathematics Subject Classification ID: 17B69
Mathematics Subject Classification ID: 17B40
Mathematics Subject Classification ID: 94B99
zbMATH DE Number: 1475244
zbMATH Keywords: code vertex operator algebra
zbMATH Keywords: automorphism group
zbMATH Keywords: extended binary Hamming code
zbMATH Keywords: Mathieu group
reviewed by: Xiaoping Xu
MaRDI profile type: Publication
full work available at URL: jabr.1999.8255
OpenAlex ID: W1995272140
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DOI: 10.1006/JABR.1999.8255
description: scientific article; zbMATH DE number 1475244