On abelian (22m+1(2m-1+ 1), 2m(2m+ 1), 2m)-difference sets

Authors:
K. T. Arasu;Yu Qing Chen;Alexander Pott
Affiliations:
Department of Mathematics and Statistics, Wright State University, Dayton, OH;Department of Mathematics and Statistics, Wright State University, Dayton, OH;Institute for Algebra and Geometry, Otto-von-Guericke-University Magdeburg, Magdeburg, Germany
Venue:
Journal of Combinatorial Theory Series A
Year:
2006

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Abstract

In this paper we prove that an abelian group contains (22m+1 (22m-1 + 1), 2m(2m + 1), 2m)-difference sets with m ≥ 3 if and only if it contains an elementary abelian 2-group of order 22m. Our proof shows that the method of constructing such difference sets is essentially unique.