Geodesic
Difference sets with $n=2p^m$
Journal of Algebraic Combinatorics, Tome 7 (1998) no. 1, pp. 77-89.

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Summary: Let D be a (v,k, $lambda$) difference set over an abelian group G with even n = k - $lambda$. Assume that t $isin$ N satisfies the congruences t $equiv$ q $_{i} ^{fi}$ (mod $exp(G))$ for each prime divisor q $_{i}$ of n/2 and some integer f $_{i}$. In [4] it was shown that t is a multiplier of D provided that n > $lambda$, (n/2, $lambda$) = 1 and (n/2, v) = 1. In this paper we show that the condition n > $lambda$ may be removed. As a corollary we obtain that in the case of n= 2p $^{a}$ when p is a prime, p should be a multiplier of D. This answers an open question mentioned in [2].
Keywords: difference set, abelian group 
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     title = {Difference sets with $n=2p^m$},
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Muzychuk, Mikhail. Difference sets with $n=2p^m$. Journal of Algebraic Combinatorics, Tome 7 (1998) no. 1, pp. 77-89. http://geodesic.mathdoc.fr/item/JAC_1998__7_1_a1/