Difference Sets over the Galois RingGR(2n, 2)

We show there exist two infinite families of difference sets with the parameters 22n, 2n − 1(2n ± 1), 2n − 1(2n − 1 ± 1) over the Galois ring GR(2n, 2), according to whether n is an odd or even integer. Namely, for every characteristic 2n, there exists a difference set over the Galois ringGR (2n, 2).