Hamming graphs in Nomura algebras

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Abstract

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
Volume435
Issue number2
DOIs
Publication statusPublished - 2011 Jul 15

Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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