Hamming graphs in Nomura algebras

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Let A be an association scheme on q ≥ 3 vertices. We show that the Bose-Mesner algebra of the generalized Hamming scheme H(n,A), for n ≥ 2, is not the Nomura algebra of any type II matrix. This result gives examples of formally self-dual Bose-Mesner algebras that are not the Nomura algebras of type II matrices.

Original languageEnglish
Pages (from-to)330-341
Number of pages12
JournalLinear Algebra and Its Applications
Issue number2
Publication statusPublished - 2011 Jul 15


  • Duality of association scheme
  • Hamming scheme
  • Nomura algebra
  • Type II matrix


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