New partial difference sets in Z(p2)(t) and a related problem about Galoisrings

We generalize a construction of partial difference sets (PDS) by Chen, Ray- Chaudhuri, and Xiang through a study of the Teichmuller sets of the Galois rings. Let R = GR(p(2), t) be the Galois ring of characteristic p(2) and ra nk t with Teichmuller set T and let pi: R --> R/pR be the natural homomorph ism. We give a construction of PDS in R with the parameters nu = p(2t), k = r(p(t) - 1), lambda = p(t) + r(2) - 3r, mu = r(2) - r, where r = lp(t-s(p, t)), 1 less than or equal to l less than or equal to p(s(p,t)), and s(p, t) is the largest dimension of a GF(p)-subspace W subset of R/pR such that pi (-1)(W)boolean ANDT generates a subgroup of R of rank < t. We prove that s (p,T) is the largest dimension of a GF(p)-subspace W of GF(p(t)) such that dim W-p < t, where W-p is the GF(p)-space generated by {Pi (p)(i = 1) w(i)\ w(i) epsilon W, 1 less than or equal to i less than or equal to p}. We dete rmine the values of s(p, t) completely and solve a general problem about di m(E) W-r for an E-vector space W in a finite extension of a finite field E. The PDS constructed here contain the family constructed by Chen, Ray-Chaud huri, and Xiang and have a wider range of parameters. (C) 2000 Academic Pre ss.