A *signed (v,k,λ)-difference set* in a group *G* of order *v* is a subset *{d _{1}, d_{2}, …, d_{k}}* of

*G*and signs

*s*in

_{i}*{-1,1}*such that the element

*D = Σ s*in the group ring

_{i}d_{i}*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.