Construction of Difference Sets from Unions of Cyclotomic Classes of Order N=14

Abstract

Let G be an additive group of order v, D be a non-empty proper k-subset of G, and λ be any integer. Then D is a (v, k, λ) - difference set if every nonzero element of the group can be expressed as a difference d1 - d2 of elements of D in exactly λ ways. Let q be a prime of the form q = nN + 1 for integers n>1 and N>1. For q0(14, q) ∪ C2(14, q) ∪ C4(14, q) ∪ C6(14, q) ∪ C8(14, q) ∪ C10(14, q) ∪ C12(14, q) forms a quadratic cyclotomic difference set. Similarly, this union together with zero forms a difference set equivalent to the modified quadratic cyclotomic difference sets.