New Partial Difference Sets in tp2 and a Related Problem about Galois Rings

We generalize a construction of partial difference sets (PDS) by Chen, Ray-Chaudhuri, and Xiang through a study of the Teichmüller sets of the Galois rings. Let R=GR(p2, t) be the Galois ring of characteristic p2 and rank t with Teichmüller set T and let π:R→R/pR be the natural homomorphism. We give a construction of PDS in R with the parameters ν=p2t, k=r(pt−1), λ=pt+r2−3r, μ=r2−r, where r=lpt−s(p, t), 1≤l≤ps(p, t), and s(p, t) is the largest dimension of a GF(p)-subspace W R/pR such that π−1(W)∩T generates a subgroup of R of rank