Families of weighing matrices
- 1 February 1974
- journal article
- research article
- Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society
- Vol. 10 (1) , 119-122
- https://doi.org/10.1017/s0004972700040703
Abstract
A weighing matrix is an n × n matrix W = W(n, k) with entries from {0, 1, −1}, satisfying = WWt = KIn. We shall call k the degree of W. It has been conjectured that if n ≡ 0 (mod 4) then there exist n × n weighing matrices of every degree k ≤ n.We prove the conjecture when n is a power of 2. If n is not a power of two we find an integer t < n for which there are weighing matrices of every degree ≤ t.Keywords
This publication has 2 references indexed in Scilit:
- Combinatorics: Room Squares, Sum-Free Sets, Hadamard MatricesLecture Notes in Mathematics, 1972
- (1,2,4,8)-sums of squares and Hadamard matricesProceedings of Symposia in Pure Mathematics, 1971