Nonexistence of certain supplementary difference sets

This paper finds restrictions on the parameters of supplementary difference sets in any group G with a subgroup of index 2, which therefore includes all cyclic groups of even orders. As a corollary to the main theorem, we have that if S₁, …, S_r are r − {2v, k₁, …, k_r; 2λ} supplementary difference sets in such a group, then not all of v, k₁, …, k_r, λ are odd; also [formula omitted] is the sum of r squares.