Tactical (de-)compositions of symmetric configurations

We introduce a new method to describe tactical (de-)compositions of symmetric configurations via block ( 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 ( 2 p 2 ) p + s where p is any prime and s ≤ t is a positive integer such that t − 1 is the greatest prime power with t 2 − t + 1 ≤ p . In particular, we obtain a new configuration 9810.