Cyclic Relative Difference Sets and Their p-Ranks
Date
2002
Authors
Journal Title
Journal ISSN
Volume Title
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.
Description
Keywords
Affine GMW difference set, Gauss sum, Relative difference set, Singer difference set, Stickelberger’s theorem, Teichmuller character