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.

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