Abstract
In this paper we show that for any fusion \(\mathcal {B}\) of an association scheme \(\mathcal {A}\), the generalized Hamming scheme \(H(n,\mathcal {B})\) is a nontrivial fusion of \(H(n,\mathcal {A})\). We analyze the case where \(\mathcal {A}\) is the association scheme on a strongly-regular graph, and determine the parameters of all strongly-regular graphs for which the generalized Hamming scheme, \(H(2,\mathcal {A})\), has extra fusions, in addition to the one arising from the trivial fusion of \(\mathcal {A}\).
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