Using rational idempotents to show Turyn's bound is sharp
Davis, Dillon, and Jedwab all showed the existence of difference sets in groups C2r+2 x C-2r. Turyn's bound had previously shown that abelian 2-groups with higher exponents could not admit difference sets. We give a new construction technique that utilizes character values, rational idempotents, and tiling structures to produce Hadamard difference sets in the group C2r+2 x C-2r to replicate the result.
turyn's bound difference set hadamard menon