| 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. |
