FOUR CIRCULANT HADAMARD MATRICES



© Nickolay Balonin and Jennifer Seberry, 1.05.2014

Hadamard matrix catalogue and on-line algorithms


There is Ryser's conjecture (see [1], page 134): is the inexistence of matrices of order n > 4 that are circulant and Hadamard matrices simultaneously. Now we are interesting in symmetric four- or fifth-circulant Hadamard matrices of rich structure (circulant and back-circulant blocks).



Two four circulant matrices H8



Two four-circulant matrices H12



Two four-circulant matrices H16



Four-circulant matrix H20 and H24



Four-circulant matrices H28



Four-circulant matrices H32 and H36



Fifth-circulant matrix H40 and H48



Four-circulant matrix H52



Four-circulant matrices H60 and H64

Note: matrices H24, H40 have 5 different cells (!)


1. H. J. Ryser, Combinatorial mathematics. The Carus Mathematical Monographs, No. 14, Published by The Mathematical Association of America; distributed by John Wiley and Sons, Inc., New York 1963.

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