Design theory
Gauss sums, Jacobi sums, and p-ranks of cyclic difference sets
Journal of Combinatorial Theory Series A
A New Family of Ternary Sequences with IdealTwo-level Autocorrelation Function
Designs, Codes and Cryptography
The invariant factors of some cyclic difference sets
Journal of Combinatorial Theory Series A
Some Notes on d-Form Functions with Difference-Balanced Property
WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
On the ranks of bent functions
Finite Fields and Their Applications
Recent progress in algebraic design theory
Finite Fields and Their Applications
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By modifying the constructions in Helleseth et al. [10] and No [15], we construct a family of cyclic ((q3k−1)/(q−1), q−1, q3k−1, q3k−2) relative difference sets, where q=3e. These relative difference sets are “liftings” of the difference sets constructed in Helleseth et al. [10] and No [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.