Cyclic Relative Difference Sets and Their p-Ranks

Date
2002
Authors
Chandler, D.B.
Xiang, Qing
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
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