scholarly journals Skew Hadamard Difference Sets

2020 ◽  
pp. 215-231
Keyword(s):  
Difference Sets ◽  
Skew Hadamard 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.

scholarly journals Inequivalence of Skew Hadamard Difference Sets and Triple Intersection Numbers Modulo a Prime

10.37236/3762 ◽  
2013 ◽  
Vol 20 (4) ◽  
Author(s):  
Koji Momihara
Keyword(s):  
Abelian Groups ◽  
Difference Sets ◽  
Intersection Numbers ◽  
Skew Hadamard Difference Sets ◽  
Triple Intersection ◽  
New Construction ◽  
Hadamard Difference Sets

Recently, Feng and Xiang found a new construction of skew Hadamard difference sets in elementary abelian groups. In this paper, we introduce a new invariant for equivalence of skew Hadamard difference sets, namely triple intersection numbers modulo a prime, and discuss inequivalence between Feng-Xiang skew Hadamard difference sets and the Paley difference sets. As a consequence, we show that their construction produces infinitely many skew Hadamard difference sets inequivalent to the Paley difference sets.

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