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University of Wollongong

1971

Articles 1 - 6 of 6

Full-Text Articles in Physical Sciences and Mathematics

A Skew-Hadamard Matrix Of Order 92, Jennifer Seberry Jan 1971

A Skew-Hadamard Matrix Of Order 92, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

Previously the smallest order for which a skew-Hadamard matrix was not known was 92. We construct such a matrix below.


Some (1, -1) Matrices, Jennifer Seberry Jan 1971

Some (1, -1) Matrices, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

We define an n-type (1, -1) matrix N = 1 + R of order n ~ 2 (mod 4) to have R symmetric and R2 = (n - 1)/n. These matrices are analogous to skewtype matrices M = 1 + W which have W skew-symmetric.


Amicable Hadamard Matrices, Jennifer Seberry Jan 1971

Amicable Hadamard Matrices, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

If X is a symmetric Hadamard matrix, Y is a skew-Hadamard matrix, and XYT is symmetric, then X and Y are said to be amicable Hadamard matrices. A construction for amicable Hadamard matrices is given, and then amicable Hadamard matrices are used to generalize a construction for skew-Hadamard matrices.


Combinatorial Matrices, Jennifer Seberry Jan 1971

Combinatorial Matrices, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

We investigate the existence of integer matrices B satisfying the equation BBT = rI + sJ where T denotes transpose, r and s are integers, I is the identity matrix and J is the matrix with every element +1.


Some Results On Configurations, Jennifer Seberry Jan 1971

Some Results On Configurations, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

A (v, k, lambda) configuration is conjectured to exist for every v, k and lambda satisfying lambda(v-l) = k(k-l) and k - lambda is a square if v is even, x2 = (k - lambda)y2+(-1)(v-1)/2lamdaZ2 has a solution in integers x,y and z not all zero for v odd.


Integer Matrices Obeying Generalized Incidence Equations, Jennifer Seberry Jan 1971

Integer Matrices Obeying Generalized Incidence Equations, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

We consider integer matrices obeying certain generalizations of the incidence equations for (v, k, lambda)-configurations and show that given certain other constraints, a constant multiple of the incidence matrix of a (v, k, lambda)-configuration may be identified as the solution of the equation.