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A note on balanced weighing matrices

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Part of the Lecture Notes in Mathematics book series (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.

Keywords

  • Abelian Group
  • Incidence Matrix
  • Orthogonal Matrice
  • Hadamard Matrice
  • Group Matrix

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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).

    CrossRef  MATH  Google Scholar 

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

    CrossRef  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 

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© 1975 Springer-Verlag

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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

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

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07154-9

  • Online ISBN: 978-3-540-37482-4

  • eBook Packages: Springer Book Archive