Abstract
In this paper, we will give a construction of a family of(4q^{2n+2}\frac{q^{2n+2}-1}{q^2-1} ,q^{2n+1}[\frac{2(q^{2n+2}-1)}{q+1}+1] , ( q^{2n+2}-q^{2n+1})\frac{q^{2n+1}+1}{q+1})-difference sets in the group K\times G, where q is any power of2 , K is any group with|K|=\frac{q^{2n+2}-1}{q^2-1} and G is an abelian2 -group of order 4q^{2n+2} which contains an elementary abelian subgroup of index 2.
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