Classification of skew‐Hadamard matrices of order 32 and association schemes of order 31

2020 ◽  
Vol 28 (6) ◽  
pp. 421-427
Author(s):  
Akihide Hanaki ◽  
Hadi Kharaghani ◽  
Ali Mohammadian ◽  
Behruz Tayfeh‐Rezaie
Keyword(s):  
Hadamard Matrices ◽  
Association Schemes

scholarly journals On some recent progress in the classification of $$(P\hbox { and }Q)$$-polynomial association schemes

2019 ◽  
Author(s):  
Alexander L. Gavrilyuk ◽  
Jack H. Koolen
Keyword(s):  
Symmetric Spaces ◽  
Recent Progress ◽  
Association Schemes ◽  
Compact Symmetric Spaces ◽  
Expository Paper

AbstractThe problem of classification of $$(P\hbox { and }Q)$$(PandQ)-polynomial association schemes, as a finite analogue of E. Cartan’s classification of compact symmetric spaces, was posed in the monograph “Association schemes” by E. Bannai and T. Ito in the early 1980s. In this expository paper, we report on some recent results towards its solution.

scholarly journals Butson-type complex Hadamard matrices and association schemes on Galois rings of characteristic 4

2018 ◽  
Vol 6 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Takuya Ikuta ◽  
Akihiro Munemasa
Keyword(s):  
Association Scheme ◽  
Hadamard Matrix ◽  
Hadamard Matrices ◽  
Association Schemes ◽  
Roots Of Unity ◽  
Galois Rings ◽  
Type Complex ◽  
Complex Hadamard Matrix

Abstract We consider nonsymmetric hermitian complex Hadamard matrices belonging to the Bose-Mesner algebra of commutative nonsymmetric association schemes. First, we give a characterization of the eigenmatrix of a commutative nonsymmetric association scheme of class 3 whose Bose-Mesner algebra contains a nonsymmetric hermitian complex Hadamard matrix, and show that such a complex Hadamard matrix is necessarily a Butson-type complex Hadamard matrix whose entries are 4-th roots of unity.We also give nonsymmetric association schemes X of class 6 on Galois rings of characteristic 4, and classify hermitian complex Hadamard matrices belonging to the Bose-Mesner algebra of X. It is shown that such a matrix is again necessarily a Butson-type complex Hadamard matrix whose entries are 4-th roots of unity.

scholarly journals Classification of association schemes of small order

2003 ◽  
Vol 264 (1-3) ◽  
pp. 75-80 ◽  
Author(s):  
A. Hanaki ◽  
I. Miyamoto
Keyword(s):  
Association Schemes

On the classification of Hadamard matrices of order 32

2010 ◽  
Vol 18 (5) ◽  
pp. 328-336 ◽  
Author(s):  
H. Kharaghani ◽  
B. Tayfeh-Rezaie
Keyword(s):  
Hadamard Matrices
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