Tiling Groups with Difference Sets
Keyword(s):
We study tilings of groups with mutually disjoint difference sets. Some necessary existence conditions are proved and shown not to be sufficient. In the case of tilings with two difference sets we show the equivalence to skew Hadamard difference sets, and prove that they must be normalized if the group is abelian. Furthermore, we present some constructions of tilings based on cyclotomy and investigate tilings consisting of Singer difference sets.
2006 ◽
Vol 113
(7)
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pp. 1526-1535
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2011 ◽
Vol 118
(1)
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pp. 27-36
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2008 ◽
Vol 50
(1)
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pp. 93-105
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2012 ◽
Vol 119
(1)
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pp. 245-256
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2007 ◽
Vol 114
(5)
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pp. 867-887
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