Constructions of Partial Difference Sets and Relative Difference Sets Using Galois Rings II

In a previous paper, [Des., Codes and Cryptogr.8(1996), 215–227]; we used Galois rings to construct partial difference sets, relative difference sets and a difference set. In the present paper, we first generalize and improve the construction of partial difference sets in [Des., Codes and Cryptogr.8(1996), 215–227]; also we obtain a family of relative difference sets from these partial difference sets. Second, we construct a class of relative difference sets in (Z4)2m+1⊕(Z4)r⊕(Z2⊕Z2)s,r+s=m, r, s⩾0 with respect to a subgroup (Z2)2m+1. These constructions make use of character sums from Galois rings, and relate relative difference sets to Hadamard difference sets.