COMMON PROPUS

A
 BR 
 CR 
 DR 
 CR 
 DT
 –A 
 –BT
 BR 
 –A 
 –DT
 CT
 DR 
 –CT
 BT
 –A 


© Nickolay A. Balonin, Dragomir Z. Djokovic 10.01.2015

Common Propus-Hadamard matrices:
CP(A,B=C,D)


Dragomir Z. Djokovic: the common propus Hadamard matrices of order 4n=q+1 exist whenever q is a prime power congruent to 3 mod 8. In particular they exist when n is:

11, 17, 33, 35, 53, 71, 77, 83, 123, 125.


The good-propus Hadamard matrices of orders 92 (v=23), 116 (v=29) and 172 (v=43 *)) were found and presented [1].

[1] Olivia Di Matteo, Dragomir Z. Djokovic, Ilias S. Kotsireas, Symmetric Hadamard matrices of order 116 and 172 exist, 2015 http://arxiv.org/abs/1503.04226.

*) We can use a symmetric D-optimal Design 86 and Legendre symbols.




SDS LIBRARY

STARTING MATRICES TO 100



Matrices C10 and H20



Matrices C14 and H28



Matrices C18 and H36

DRAGOMIR'S AND NICK'S H44





Two good-propus matrices Dragomir's and Nick's H44



Matrices C26 and Nick's H52 !!



Matrices C30 and Nick's H60



Reversed version C30 and Nick's H60



Dragomir's matrix GP68 (look C30 cells!)



Matrices C38 and H76



Matrices C42 and H84



Matrix H92 see [1]



Matrices C50 and H100

COLOUR BIG MATRICES



Matrix H116 see [1]



Matrix GP132 (n=33)



Matrix GP140 (n=35)



Matrix GP212 (n=53)



Matrix GP284 (n=71)



Matrix GP308 (n=77)



Matrix GP332 (n=83)



Matrix GP492 (n=123)





Matrices A, B, D of GP500 (n=125)


Nick: there is "a law" of vitrage-inertion: two-circulant conference matrices are vitrages based on H2, the first cell is "light modified" J–2×I. Propus-matrices use these cells, so H68 has common codes with C30. Inertion of cells well seen on the pictures below. Fourier operator, it is waves, vitrages – waves inside little squares, so pictures of cells are similar.



TWO-CIRCULANT CONFERENCE MATRICES

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