On abelian (2(2m+1)(2(m-1)+1), 2(m)(2(m)+1), 2(m))-difference sets

摘要

In this paper we prove that an abelian group contains (2(2m+1)(2(m-1) + 1), 2(m)(2(m) + 1), 2(m))-difference sets with m >= 3 if and only if it contains an elementary abelian 2-group of order 2(2m). Our proof shows that the method of constructing such difference sets is essentially unique. (c) 2006 Elsevier Inc. All rights reserved.