| This paper presents new constructions of nested partial difference sets in Zpr 2t where p is any odd prime, and r and t are any positive integers. For the case where r > 2 many of these partial difference sets have parameters for which no other constructions are known to exist. The constructions make use of the structure of the Galois ring GR(pr, t), and in particular, the ring GR(pr, t) x GR(pr, t). The paper also has a discussion of Hadamard difference sets and possible connections with Galois rings, and concludes with some open related problems. |
