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
D.A. Drake, "Partial λ-geometries and generalised Hadamard matrices over groups, Canad. J. Math. 31 (1979), 617–627.
Warwick de Launey, Ph.D. Thesis, University of Sydney (in preparation).
N. Jacobson, Lectures in Abstract Algebra Vol. 2, D. Van Nostrand Company. Inc., Princeton, 1953.
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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