HADAMARD MATRICES H40 © Nickolay A. Balonin,Dragomir Z. Djokovic 10.01.2015 Dragomir has done the classification of PerGol of length 20. There are 34 equivalence classes. Only two of the classes contain pairs with symmetry (8,8). There is no pair having at lest one of the sequences with symmetry >8. So, nick's conjecture has been verified for order 40.
MAXIMUM SYMMETRY MATRIX Matrices H_{40} with index symmetry 8,8 When v=20, in addition to Nick's example: A={0,4,6,7,9,12,13,14,16}, B={2,7,8,9,10,13,18} with symmetry (8,8), there is one more equivalence class which contains such a pair. This other pair is: A={0,4,6,7,8,9,13,14,16}, B={2,7,9,10,12,13,18}.
Matrices H_{40} with index symmetry 5,5 The following periodic Golay pair (for v=20) A={0,1,2,3,6,9,11,13,17}, B={4,5,6,9,11,12,16} has the symmetry type (5,5) and this is true for ALL pairs in its equivalence class. This is a unique class with this property.
DRAGOMIR'S SDSLIBRARY
EQUIVALENCE CLASSES  MATRICES H16  MATRICES H32

