A technique for constructing divisible difference sets

Abstract

An (m, n, k, λ1,λ2) divisible difference set in a groupG of ordermn relative to a subgroupN of ordern is ak-subsetD ofG such that the list {xy−1:x, y e D} contains exactly λ1 copies of each nonidentity element ofN and exactly λ2 copies of each element ofG N. It is called semi-regular ifk > λ1 and k2=mnλ2. We develop a method for constructing a divisible difference set as a product of a difference set and a relative difference set or a difference set and a subset ofG which we call a relative divisible difference set. The method results in several parametrically new families of semi-regular divisible difference sets.