scholarly journals Generalized constructions of Menon-Hadamard difference sets

2020 ◽  
Vol 61 ◽  
pp. 101601
Author(s):  
Koji Momihara ◽  
Qing Xiang
Keyword(s):  
Difference Sets ◽  
Hadamard Difference Sets

scholarly journals Tiling Groups with Difference Sets

10.37236/5157 ◽  
2015 ◽  
Vol 22 (2) ◽  
Author(s):  
Ante Ćustić ◽  
Vedran Krčadinac ◽  
Yue Zhou
Keyword(s):  
Difference Sets ◽  
Skew Hadamard Difference Sets ◽  
Existence Conditions ◽  
Hadamard Difference Sets ◽  
Necessary Existence

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.

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