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.
- Duality of association scheme
- Hamming scheme
- Nomura algebra
- Type II matrix