Menon Hadamard Difference Sets and Regular Hadamard Matrices

2020 ◽  
pp. 159-174
Keyword(s):  
Difference Sets ◽  
Hadamard Matrices ◽  
Hadamard Difference Sets

scholarly journals Cocyclic Hadamard matrices and difference sets

2000 ◽  
Vol 102 (1-2) ◽  
pp. 47-61 ◽  
Author(s):  
Warwick de Launey ◽  
D.L. Flannery ◽  
K.J. Horadam
Keyword(s):  
Difference Sets ◽  
Hadamard Matrices

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 A class of cyclic (v; k1, k2, k3; λ) difference families with v ≡ 3 (mod 4) a prime

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Dragomir Ž. Ðokovic ◽  
Ilias S. Kotsireas
Keyword(s):  
Difference Sets ◽  
Hadamard Matrices ◽  
Difference Families ◽  
First Time

AbstractWe construct several new cyclic (v; k1, k2, k3; λ) difference families, with v ≡ 3 (mod 4) a prime and λ = k1 + k2 + k3 − (3v − 1)/4. Such families can be used in conjunction with the well-known Paley-Todd difference sets to construct skew-Hadamard matrices of order 4v. Our main result is that we have constructed for the first time the examples of skew Hadamard matrices of orders 4 · 239 = 956 and 4 · 331 = 1324.

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