Thursday, December 6, 2012 - 12:00 to 12:50

### Abstract or Additional Information

The general theme is that of constructing symmetric designs. It is often possible to accomplish this by working with two combinatorial structures, neither of which is a 2-design, but which act jointly to allow the construction of a 2-design. Such design pairs offer an expression of certain integers that are equal to 3 mod 4 as a sum of two square moduli of cyclotomic integers. It is on occasion also possible to use the Seidel-Goethals' method to construct Hadamard matrices, with such design pairs playing a central role.