Difference sets over Galois rings with odd extension degrees and characteristic an even power of 2
We construct an infinite family of (2 (ns) , 2 (ns/2 -1)(2 (ns/2)-1), 2 (ns/2 -1)(2 (ns/2 -1) -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.
difference set galois ring gauss sum