Constructions of partial difference sets and relative difference sets using Galois Rings II

Abstract

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. © 1996 Academic Press, Inc.