A strongly regular decomposition of the complete graph and its association scheme

For any positive integer m, the complete graph on 22m(2m+2) vertices is decomposed into 2m+1 commuting strongly regular graphs, which give rise to a symmetric association scheme of class 2m+2−2. Furthermore, the eigenmatrices of the symmetric association schemes are determined explicitly. As an application, the eigenmatrix of the commutative strongly regular decomposition obtained from the strongly regular graphs is derived.