TWO BORDERS TWO CIRCULANT MATRICES
© Nickolay Balonin, 1.05.2015
Conference matrix catalogue and on-line algorithms
Two borders and two circulant A,B-matrices have: A is circulant and symmetry, block B based on the two flip-inversed sequences (to be the same quantity of invariants symmetric matrices have). Two circulant core is a shadow matrix.
THE FORK C62 – ... – C74
N. A. Balonin, Jennifer Seberry A Review and New Symmetric Conference Matrices //Informatsionno-upravliaiushchie sistemy, 2014, № 4 (71), pp. 2–7.
C66 has to be between given orders!
The work with symmetries of bicycles brings method to find conference matrices C62, C74 fast in 20 minuts ! It is a fork for famous order 66. If during a night we see no C66 (for 46 we see a distantion), i'm afraid, this form does not exist the same as two circulant, four circulant or multicirculant matrices: they exist for cases 6, 26 (not for 46, 66, 86!). Let us note: 66 has to be a symmetric matrix with 33×33-block A, while 32 is the last two circulant symmetric Hadamard matrix (these circumstances can be connected by a structure bound).
Matrices C6 and C10
Matrices C14 and C18
Matrices C26 and C30
Matrices C38 and C42
Matrices С50 and С54
Matrices С62 and С74
Core of Dragomir's C80
With piece of code: grainTWO CIRCULANT MATRICES