Signed Difference Sets

A signed (v,k,λ)-difference set in a group G of order v is a subset {d₁, d₂, …, d_k} of G and signs s_i in {-1,1} such that the element D = Σ s_i d_i in the group ring Z[G] satifies the difference set equation:

D D^-1 = n + λ G,

where n = k-λ.

A forthcoming paper in Designs, Codes and Cryptography defines these sets and proves many existence results about them. Rather than presenting them in a database like the other combinatorial objects on this site, they have been put in a Jupyter Notebook, containing the dataset and some simple code to handle it. The repository is at:

The Jupyter Notebook may be run online using binder by clicking here:

Note that binder can take a few minutes the first time you start it up.