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Williamson matrices of even order

Contributed Papers

Part of the Lecture Notes in Mathematics book series (LNM,volume 403)

Abstract

Recent advances in the construction of Hadamard matrices have depended on the existence of Baumert-Hall arrays and Williamson-type matrices. These latter are four (1,-1) matrices A,B,C,D, of order m, which pairwise satisfy (i) MNT = NMT, M,N ε {A,B,C,D}, and (ii) AAT+BBT+CCT+DDT = 4mIm, where I is the identity matrix. Currently Williamson matrices are known to exist for all orders less than 100 except: 35,39,47,53,59,65,67,70,71,73,76,77,83,89,94. This paper gives two constructions for Williamson matrices of even order, 2n. This is most significant when no Williamson matrices of order n are known. In particular we give matrices for the new orders 2.39,2.203,2.303,2.333,2.689,2.915, 2.1603.

Keywords

  • Prime Power
  • Incidence Matrix
  • Hadamard Matrice
  • Hadamard Matrix
  • Incidence Matrice

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

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© 1974 Springer-Verlag

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Wallis, J.S. (1974). Williamson matrices of even order. In: Holton, D.A. (eds) Combinatorial Mathematics. Lecture Notes in Mathematics, vol 403. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0057387

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  • DOI: https://doi.org/10.1007/BFb0057387

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06903-4

  • Online ISBN: 978-3-540-37837-2

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