# On the Existence of Abelian Hadamard Difference Sets and a New Family of Difference Sets

@article{Chen1997OnTE, title={On the Existence of Abelian Hadamard Difference Sets and a New Family of Difference Sets}, author={Yu Qing Chen}, journal={Finite Fields and Their Applications}, year={1997}, volume={3}, pages={234-256} }

We present a construction of Hadamard difference sets in abelian groups of order 4p4n, whose Sylowp-subgroups are elementary. By a standard composition procedure, we can now conclude that (4h2, 2h2?h,h2?h)-Hadamard difference sets exist forh= 2?13?2u2, where ?1, ?2= 0 or 1 anduis a positive integer. We then generalize the construction of Hadamard difference sets to construct a family of (4q2n(q2n? 1)/(q2?1),q2n?12(q2n? 1)/(q+ 1) + 1], (q2n?q2n?1)(q2n?1 + 1)/(q+ 1)-difference sets, whereqis an… Expand

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