Some results on skew Hadamard difference sets
In this paper, we present two constructions of divisible difference sets based on skew Hadamard difference sets. A special class of Hadamard difference sets, which can be derived from a skew Hadamard difference set and a Paley type regular partial difference set respectively in two groups of orders v (1) and v (2) with |v (1) - v (2)| = 2, is contained in these constructions. Some result on inequivalence of skew Hadamard difference sets is also given in the paper. As a consequence of Delsarte's theorem, the dual set of skew Hadamard difference set is also a skew Hadamard difference set in an abelian group. We show that there are seven pairwisely inequivalent skew Hadamard difference sets in the elementary abelian group of order 3(5) or 3(7), and also at least four pairwisely inequivalent skew Hadamard difference sets in the elementary abelian group of order 3(9). Furthermore, the skew Hadamard difference sets deduced by Ree-Tits slice symplectic spreads are the dual sets of each other when q a parts per thousand currency sign 3(11).
skew hadamard difference sets hadamard difference sets partial difference sets