Browsing by Author "Chandler, D.B."
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Item Cyclic Relative Difference Sets and Their p-Ranks(Department of Mathematical Sciences, 2002) Chandler, D.B.; Xiang, QingBy 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.Item The Invariant Factors of Some Cyclic Difference Sets(Department of Mathematical Sciences, 2002) Chandler, D.B.; Xiang, QingUsing the Smith normal forms of the symmetric designs associated with the HKM and Lin difference sets, we show that not only are these two families of difference sets inequivalent, but also that the associated symmetric designs are nonisomorphic.