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
With piece of code: grainTWO CIRCULANT MATRICES