CONFERENCE MATRIX C3646

© Nickolay Balonin 1.05.2014

Conference matrix catalogue and on-line algorithms




STARTING CELLS A,B,C



RICH CELLS of {1,2,0}-TYPES (CIRCULANT, BACK-CIRCULANT AND CROSS-SHIFTED)



POOR CELLS of {1,1,0}-TYPES (CIRCULANT AND CROSS-SHIFTED)


The Seberry construction of CORE C3646=circul(A,B,C,C',B') calculated through the A,B,C-iterations for orders n=45*92k+1 by the following formulaes

A=A⊗A⊗A+A⊗I⊗J+I⊗J⊗A+J⊗A⊗I
B=B⊗Bs⊗Bs+C⊗Bd⊗Bs–B⊗Cd⊗Bd+C⊗Cs⊗Bd
C=B⊗Bs⊗Cd+C⊗Bd⊗Cd+B⊗Cd⊗Cs–C⊗Cs⊗Cs


where I – identity matrix, J – matrix with 1, Bs=(B+B')/2, Bd=(B–B')/2, Cs=(C+C')/2, Cd=(C–C')/2, it is started at matrices of rich cell-structure: A – a circulant matrix of circulant cells (1-type), B – a circulant matrix of back-circulant cells (2-type), C – a cross-matrix (0-type): it gives Balonin-Seberry construction (below).







Matrices A, B, C of rich-structure C3646



COMPILATION THE STARTING C46 WITH INVARIANT 5



OLD AND NEW STRUCTURES (5 IS QUANTITY OF CELL-and-BLOCK TYPES)

R. Mathon. Symmetric conference matrices of order pq2+1 Canad. J. Math 30 (2), 321-331
Jennifer Seberry, Albert L. Whiteman New Hadamard matrices and conference matrices obtained via Mathon's construction, Graphs and Combinatorics, 4, 1988, 355-377.

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

ON LINE ALGORITHMS | HIDDEN CIRCULANT CELLS

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