Conference matrix catalogue and on-line algorithms

THE RICH CELL-STRUCTURE

Balonin-Seberry construction of Maton's type matrix C442=C(A,B1,B2,B3,C) has rich cell-structure: A is a circulant matrix of circulant cells (1-type), blocks B1, B2, B3 are circulant matrices of shifted back-circulant cells (2-type), C is a cross-matrix (0-type), the core of order n=q^{2}(q+2), where q+2 is order of a core, q=7, cells A, C, B1, B2, B3 given by pictures below.

A of circulant cells (1-type), C is cross-matrix (0-type)

Matrices of back-circulant cells: B1, B2, B3 (2-type)

R. Mathon. Symmetric conference matrices of order pq^{2}+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.