Tactical (de-)compositions of symmetric configurations

We introduce a new method to describe tactical (de-)compositions of symmetric configurations via block (0,1)(0,1)-matrices with constant row and column sum having circulant blocks. This method allows us to prove the existence of an infinite class of symmetric configurations of type (2p2)p+s(2p2)p+s where pp is any prime and s≤ts≤t is a positive integer such that t−1t−1 is the greatest prime power with t2−t+1≤pt2−t+1≤p. In particular, we obtain a new configuration 9810.