BEGINNING HADAMARD MATRICES



© Nickolay A. Balonin, Dragomir Z. Djokovic, Jennifer Seberry, 1.05.2014

Hadamard matrix catalogue and on-line algorithms




The circulant Ryser matrices H4 and H8

TWO BASE CONFIGURATIONS OF WEIGHING MATRIX


The weighing matrices W(n,n–2) will be written as Wn, for short, their matrix portraits have 3 colours for 0, 1, –1 entries.



Weighing matrix W12 (2 cells) and non symmetric H24



Weighing matrix W12 (4 cells) and symmetric H12



Skew weighing matrix W12 (2 cells) and skew H12



Two circulant matrix M12 with levels |a|=1, |b|=1/sqrt(2)

THE SYLVESTER ORDER



Two and four-circulant matrices H16

THE HADAMARD AND WEIGHING MATRIX TOGETHER



Two-circulant non symmetric Hadamard matrices H20 !



Weighing matrix W20 and non symmetric H40



Weighing matrix W20 (4 cells) and symmetric H20

THE FIRST SPECIAL ORDER 24



Multi-circulant non symmetric matrices W24 and H24



Multi-circulant matrices W24 and H24



Two-circulant multi-level matrix M24

THE WEIGHING MATRIX AGAIN



Weighing matrix W28 and non symmetric H56



Weighing matrix W28 (4 cells) and symmetric H28

THE SYLVESTER ORDER 32



Two and four-circulant matrices H32

THE WEIGHING MATRIX AGAIN



Weighing matrix W36 and non symmetric H72



Weighing matrix W36 and symmetric H36



Skew Hadamard matrix and Jennifer-1969 matrix H36

THE WEIGHING MATRIX 38



Weighing matrix W38

NON SYMMETRIC HADAMARD H40



Non symmetric cells Hadamard matrix H40 and four one symmetric !

THE SPECIAL ORDERS 44 (OD44)



The skew Hadamard matrices H44!



The specific weighing matrix W44 (it does not give an Hadamard matrix)

THE SECOND SPECIAL ORDER 48



Two multi-circulant matrices H48

NON SYMMETRIC HADAMARD H52



Non symmetric cells Hadamard matrix H52



Weighing matrix W52 and non symmetric H104



Weighing matrix W52 (4 cells) and symmetric H52



Skew Hadamard matrix H52

THE THIRD SPECIAL ORDER 56



Multi-circulant non symmetric matrices W56 and H56



Four-cells symmetric matrix H56 (skew structures absent)

THE WEIGHING MATRIX AGAIN



Weighing matrix W60 (2 cells)



Weighing matrix W60 (4 cells) and symmetric H60

THE SYLVESTER ORDER 64



Two-circulant matrix H64



Four-circulant matrices H64 (French Parket)

THE PROBLEM ORDER 68



Two non regular two-circulant matrices H68 by SDS(34;16,13;12) [1]



Skew Hadamard matrix H68 and weighing W68 (independent)

THE SPECIAL ORDER 72



Non symmetric matrices W72 and H72

THE WEIGHING MATRIX AGAIN



Weighing matrix W76 (2 cells)



Weighing matrix W76 and symmetric H76

NON SYMMETRIC HADAMARD H80



Non symmetric cells Hadamard matrix H80!



The Sylvester's construction H80 and by H40

THE WEIGHING MATRIX AGAIN



Weighing matrix W84 (2 cells)



Weighing matrix W84 and symmetric H84



Non symmetric Williamson H84 by Hadi's paper

THE PROBLEM ORDER 88



Non symmetric H88 built by H44 (H96 by H48)

THE LATEST ORDERS n<100



Skew Hadamard matrices H92 and H100!





Dragomir's H100, SDS (50;22,21;18)

THE WEIGHING MATRIX AGAIN



Weighing matrix W108 (2 cells)

GALOIS FIELD PROCEDURE 2C W(n,n–2)



Rambler's Top100