Circulant Partial Hadamard Matrices: Construction via General Difference Sets and Its Application to fMRI Experiments

2018 ◽  
Author(s):  
Frederick Kin Hing Phoa ◽  
Yuan-Lung Lin ◽  
Ming-Hung Kao
Keyword(s):  
Difference Sets ◽  
Hadamard Matrices ◽  
General Difference ◽  
Partial Hadamard Matrices

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 Isolated Partial Hadamard Matrices and Related Topics

2018 ◽  
Vol 25 (02) ◽  
pp. 1850009
Author(s):  
Teodor Banica ◽  
Duygu Özteke ◽  
Lorenzo Pittau
Keyword(s):  
Hadamard Matrices ◽  
Permutation Groups ◽  
Roots Of Unity ◽  
Unitary Matrices ◽  
The Subject ◽  
Partial Hadamard Matrices

We study the partial Hadamard matrices [Formula: see text] which are isolated, under the assumption that the entries [Formula: see text] are roots of unity, or more generally, under the assumption that the combinatorics of H comes from vanishing sums of roots of unity. We first review the various conjectures on the subject, and then we present several new results, regarding notably the isolation of the master Hadamard matrices, [Formula: see text], and the structure of the isolated matrices arising via the McNulty-Weigert construction. We discuss then the notion of isolation, in some related contexts, of the magic unitary matrices, and of the quantum permutation groups.

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