Skip to main content
SpringerLink
Log in

A note on balanced weighing matrices

  • Invited Addresses
  • Conference paper
  • First Online:
Combinatorial Mathematics III

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 452))

Abstract

A balanced weighing matrix is a square orthogonal matrix of 0’s, 1’s and −1’s such that the matrix obtained by squaring entries is the incidence matrix of a (v, k, λ) configuration. Properties of cyclically generated and group generated configurations are discussed and certain natural questions arising are disposed of by theory or counter-example. Matrices of low order are tabulated.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. I. Blake, Private Communication.

    Google Scholar 

  2. A. V. Geramita, J. M. Geramita, J. S. Wallis, Orthogonal designs, Queen’s Mathematical Preprint #1973–37, Queen’s University, Kingston, Ontario (1973); Linear and Multilinear Algebra (To appear).

    Google Scholar 

  3. R. C. Mullin, Normal affine resolvable designs and orthogonal matrices, Utilitas Math. (To appear).

    Google Scholar 

  4. J. S. Wallis, Orthogonal (0, 1, −1) matrices, Proc. First Australian Conference on Combinatorial Mathematics, (TUNRA, Newcastle (1972)).

    MATH  Google Scholar 

  5. W. D. Wallis, A. P. Street and J. S. Wallis, Combinatorics: Room squares, sum-free sets and Hadamard matrices (Lecture notes in mathematics Vol. 292, Springer-Verlag, Berlin-Heidelberg-New York, 1972).

    Book  MATH  Google Scholar 

  6. D. Raghavarao, Some aspects of weighing designs, Ann. Math. Stat. 31 (1960) 878–884.

    Article  MathSciNet  MATH  Google Scholar 

  7. H. J. Ryser, Combinatorial Mathematics, Carus Monograph 14, (John Wiley and Sons, 1965).

    Google Scholar 

  8. P. J. Schellenberg, A computer construction for balanced orthogonal matrices, (To appear).

    Google Scholar 

  9. A. Speiser, Theorie der Gruppen von endliches ordnung, (Springer-Verlag, Berlin, 1937).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Combinatorics and Optimization, University of Waterloo, Ontario, Canada

    R. C. Mullin

Authors
  1. R. C. Mullin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Anne Penfold Street Walter Denis Wallis

Rights and permissions

Reprints and permissions

Copyright information

© 1975 Springer-Verlag

About this paper

Cite this paper

Mullin, R.C. (1975). A note on balanced weighing matrices. In: Street, A.P., Wallis, W.D. (eds) Combinatorial Mathematics III. Lecture Notes in Mathematics, vol 452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069541

Download citation

  • DOI: https://doi.org/10.1007/BFb0069541

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07154-9

  • Online ISBN: 978-3-540-37482-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation