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arXiv · 1907.07024

Morphisms of Skew Hadamard Matrices

Philip Heikoop·Guillermo Nuñez Ponasso·Padraig Ó Catháin·John Pugmire
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Abstract

Quaternary unit Hadamard (QUH) matrices were introduced by Fender, Kharagani and Suda along with a method to construct them at prime power orders. We present a novel construction of real Hadamard matrices from QUH matrices. Our construction recovers the result by Mukhopadhyay on the existence of real Hadamard matrices of order $q^n+q^{n-1}$ for each prime power $q\equiv 3\mod 4$. Furthermore we provide nonexistence conditions for QUH matrices.

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Philip Heikoop, Guillermo Nuñez Ponasso, Padraig Ó Catháin, John Pugmire. 2020-04-17. Morphisms of Skew Hadamard Matrices. https://arxiv.org/abs/1907.07024

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