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Some results on weighing matrices

Published online by Cambridge University Press:  17 April 2009

Jennifer Seberry Wallis  and
Albert Leon Whiteman
Jennifer Seberry Wallis
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, ACT.
Albert Leon Whiteman
Affiliation:
Department of Mathematics, University of Southern California, Los Angeles, California, USA.
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Abstract

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It is shown that if q is a prime power then there exists a circulant weighing matrix of order q2 + q + 1 with q2 nonzero elements per row and column.

This result allows the bound N to be lowered in the theorem of Geramita and Wallis that “given a square integer k there exists an integer N dependent on k such that weighing matrices of weight k and order n and orthogonal designs (1, k) of order 2n exist for every n > N”.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 12 , Issue 3 , June 1975 , pp. 433 - 447
Copyright
Copyright © Australian Mathematical Society 1975

References

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