## Cyclic Relative Difference Sets and Their p-Ranks

2002
Chandler, D.B.
Xiang, Qing
##### Publisher
Department of Mathematical Sciences
##### Abstract
By modifying the constructions in [10] and [15], we construct a family of cyclic ((q 3k − 1)/(q − 1), q − 1, q 3k − 1 , q 3k − 2 ) relative difference sets, where q = 3 e . These relative difference sets are “liftings” of the difference sets constructed in [10] and [15]. In order to demonstrate that these relative difference sets are in general new, we compute p-ranks of the classical relative difference sets and 3-ranks of the newly constructed relative difference sets when q = 3. By rank comparison, we show that the newly constructed relative difference sets are never equivalent to the classical relative difference sets, and are in general inequivalent to the affine GMW difference sets.
##### Keywords
Affine GMW difference set , Gauss sum , Relative difference set , Singer difference set , Stickelberger’s theorem , Teichmuller character