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.


N. A. Balonin, Jennifer Seberry A Review and New Symmetric Conference Matrices //Informatsionno-upravliaiushchie sistemy, 2014, № 4 (71), pp. 2–7.

THE FORK C62 – ... – C74



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).

CONFERENCE MATRICES



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: grain

TWO CIRCULANT MATRICES

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