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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