TWO CIRCULANT WEIGHING MATRICES



© Nickolay Balonin, 1.05.2015

Hadamard matrix catalogue and on-line algorithms


Теорема (Geramita and Seberry (1979), Theorem 4.46) Если существуют циклические матрицы A, B порядка n с элементами {0,1,–1}, удовлетворяющие критерию

A2+B2=wI,


то существует взвешенная матрица W=W(2n,w)

W=
A
B
 BT 
 –AT 
W=
A
 BR 
 BR 
 –A 


где R – обратная единичная матрица (флип).

SYMMETRIC STRUCTURES



Weighing matrices W(6,4) and W(12,10)



Weighing matrices W(20,18) and W(28,26)



Weighing matrices W(36,34) and W(52,50)


Two circulant weighing matrices W(2n,2n–2) with 0 along two diagonals found by the following algorithm.

SOME STRUCTURES, MORE ZEROS



Weighing matrices W(10,8) and W(10,5)



Weighing matrix W(12,8) and W(18,16)



Weighing matrices W(20,17) and W(20,16)



Weighing matrices W(22,17) and W(24,20)

COMMOM CATALOGUE



Weighing matrices W(6,4) and W(10,8)



Weighing matrix* W(12,10) and W(18,16)



Weighing matrix* W(20,18) and W(22,20)



Weighing matrix* W(28,26) and W(34,32)



Weighing matrix* W(36,34) and W(38,36)



Weighing matrix W(42,40)



Weighing matrix* W(52,50) and W(54,52)



Weighing matrices W(66,64) and W(82,80)

*) matrices, that leads to H(4n) by sylvester construction



Table of two squares sum


Olga Taussky-Todd's influence on matrix theory and matrix theorists, known her works, connected with sums of squares and Hadamard matrices. Weighing matrices much developed in works of Jennifer Seberry. Both sources start about 70-th.

TWO CIRCULANT HADAMARD MATRICES | CONFERENCE MATRICES

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