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 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.

scholarly journals Some classes of Hadamard matrices with constant diagonal

1972 ◽  
Vol 7 (2) ◽  
pp. 233-249 ◽  
Author(s):  
Jennifer Wallis ◽  
Albert Leon Whiteman
Keyword(s):  
Prime Power ◽  
Abelian Groups ◽  
Difference Sets ◽  
Hadamard Matrices ◽  
Incidence Matrices

The concepts of circulant and backcirculant matrices are generalized to obtain incidence matrices of subsets of finite additive abelian groups. These results are then used to show the existence of skew-Hadamard matrices of order 8(4f+1) when f is odd and 8f + 1 is a prime power. This shows the existence of skew-Hadamard matrices of orders 296, 592, 1184, 1640, 2280, 2368 which were previously unknown.A construction is given for regular symmetric Hadamard matrices with constant diagonal of order 4(2m + 1)2 when a symmetric conference matrix of order 4m + 2 exists and there are Szekeres difference sets, X and Y, of size m satisfying x є X ⇒ −xє X, y є Y ⇒ −y єY.

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