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Association schemes have been used in coding theory and other combinatorial problems. In this paper, we construct association schemes for the abelian groups Z₂ʳ, 〖 Z〗_ (n₁) ×Z_ (n₂) ×⋯×Z_ (nᵣ), set of n ×n matrices over Zₘ and for the general linear group of order 2 over Z₂, Z₄, and Z₆. We also obtain association schemes for symmetric groups and alternating groups of degree 4 and 5 using canonical forms.
Anuradha Sabharwal (Fri,) studied this question.