Using a class of permutation polynomials of F32h+1 obtained from the
Ree-Tits symplectic spreads in PG(3,32h+1), we construct a family of skew
Hadamard difference sets in the additive group of F32h+1. With the help
of a computer, we show that these skew Hadamard difference sets are new when
h=2 and h=3. We conjecture that they are always new when h>3.
Furthermore, we present a variation of the classical construction of the twin
prime power difference sets, and show that inequivalent skew Hadamard
difference sets lead to inequivalent difference sets with twin prime power
parameters.Comment: 18 page