New constructions of signed difference sets

Signed difference sets have interesting applications in communications and coding theory. A ( v , k , λ ) -difference set in a finite group G of order v is a subset D of G with k distinct elements such that the expressions x y - 1 for all distinct two elements x , y ∈ D , represent each non-identity element in G exactly λ times. A ( v , k , λ ) -signed difference set is a generalization of a ( v , k , λ ) -difference set D , which satisfies all properties of D , but has a sign for each element in D . We will show some new existence results for signed difference sets by using partial difference sets, product methods, and cyclotomic classes.