On Hadamard Difference Sets

This chapter discusses Hadamard difference sets. The difference set is a subset D of size k of a group G of order v such that every nonidentity element of G can be expressed as a product d 1 d 2 -1 of elements of D in exactly λ ways. A difference set D is said to be cyclic, Abelian, non-Abelian, if the group G has the corresponding property. A difference set with λ= 1 is sometimes called planar or simple. If G is an abelian group written in additive notation, the defining condition is that every nonzero element of G can be written as a difference of elements of D in exactly λ ways.