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Generalised hadamard matrices whose rows and columns form a group

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1036)

Abstract

We define a group Hadamard matrix to be a generalised Hadamard matrix whose rows form a group. We show that for abelian groups G, only group Hadamard matrices of type ps for Cp×...×Cp exist. We also show that the matrices for Cp of each possible order are unique up to equivalence.

We indicate a connection between strongly independent sets and row group Hadamard matrices.

We show that the irreducible factors of a group Hadamard matrix under tensor product are unique up to equivalence. This allows us to count and classify the group Hadamard matrices for Cp×Cp.

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References

  1. D.A. Drake, "Partial λ-geometries and generalised Hadamard matrices over groups, Canad. J. Math. 31 (1979), 617–627.

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  2. Warwick de Launey, Ph.D. Thesis, University of Sydney (in preparation).

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  3. N. Jacobson, Lectures in Abstract Algebra Vol. 2, D. Van Nostrand Company. Inc., Princeton, 1953.

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  4. Heinz Lüneburg, Translation Planes Springer-Verlag, Berlin, 1980.

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© 1983 Springer-Verlag

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De Launey, W. (1983). Generalised hadamard matrices whose rows and columns form a group. In: Casse, L.R.A. (eds) Combinatorial Mathematics X. Lecture Notes in Mathematics, vol 1036. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0071517

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  • DOI: https://doi.org/10.1007/BFb0071517

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12708-6

  • Online ISBN: 978-3-540-38694-0

  • eBook Packages: Springer Book Archive