On abelian -difference sets

In their article A. Blokhuis, D. Jungnickel and B. Schmidt (2002) [1] have shown that if an abelian ( n , n , n , 1 ) -difference set exists, then n is a power of a prime. In this article we prove that if an abelian ( 2 n , n , 2 n , 2 ) -difference set exists, then n is a power of 2 except in a few special cases. This is also a generalization of one of T. Feng and Q. Xiangʹs (2008) [2] results in the abelian case.