Hadamard matrices, Sequences, and Block Designs Page 1 University of Wollongong Research
Online Faculty of Informatics - Papers (Archive) Faculty of Engineering and Information …

An n× n matrix H with all its entries+ 1 and-1 is Hadamard if HH'= nI. It is well known that n
must be 1, 2 or a multiple of 4 for such a matrix to exist, but is not known whether Hadamard …

The purpose of this note is to point out some connexions between generalized Hadamard
matrices (4, 5) and various tactical configurations such as group divisible designs (3), affine …

It was established in (5) that the existence of a Hadamard matrix of order 4t is equivalent to
the existence of a symmetrical balanced incomplete block design with parameters v= 4t—1 …

Given any natural number q> 3 we show there exists an integer t⩽[2log 2 (q− 3)] such that
an Hadamard matrix exists for every order 2 sq where s> t. The Hadamard conjecture is that …

In this paper we are concerned with (s, r; 2, G)-difference matrices. Here G is a group of
order s and D an (rx s2)-matrix with entries from G such that the sequence d~ k-djk of …

Orthogonal Designs Page 1 Chapter 1 Orthogonal Designs An orthogonal design of order n,
type (s1,...,sl), denoted, OD(n;s1,...,sl), si positive integers, is an n×n matrix X, with entries …

1. Introduction. If plp**... p" a is the prime power decomposition of an integer v, and we
define the arithmetic function n (v) by n (v)= in (pnl, n2 nu) then it is known, MacNeish [16] …

It has been suggested that combinatorial theory is the fastest-growing area of modern
mathematics. The largest part of the subject is graph theory, as evidenced by the ever …

This Report studies Hadamard matrices of order 20. Proof is given that there are exactly
three classes of such matrices; the work done to show this result is discussed, and the …