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A Construction of Difference Sets

Authors:	Yu Qing Chen

Affiliation:	(1) Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, OH, 43210-1174

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 thegroup , where q is any power of 2, K is any group with $\|K\| = frac{{q^{2n + 2} - 1}}{{q^2 - 1}}$ and G is an abelian 2-group of order $4q^{2n + 2}$ which contains anelementary abelian subgroup of index 2.

Keywords:	difference set symmetric design
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