Design theory
Difference sets over the Galois ring G R (2n, 2)
European Journal of Combinatorics
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We construct an infinite family of (2 ns , 2 ns/2 -1(2 ns/2驴1), 2 ns/2 -1(2 ns/2 -1 驴1)) difference sets over a Galois ring GR(2 n , s) with characteristic an even power n of 2 and an odd extension degree s. It makes a chain of difference sets preserving the structures when n increases and s is fixed. We introduce a new operation into GR(2 n , s). The Gauss sum associated with the multiplicative character defined by the subgroup with respect to the new operation plays an important role in the construction.