Difference set

Summary

A difference set is a subset $D$ of a finite group with a balance property. Every non-identity element of the group arises as a "difference" $d_1 d_2^{-1}$ of elements of $D$ the same number $\lambda$ of times. The translates of a difference set form a symmetric block design on which the group acts regularly. Difference sets give many projective planes, Hadamard matrices and sequences with good correlation. The node difference set gives the precise definition.