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arXiv · 1907.02623

A new family of Hadamard matrices of order $4(2q^2+1)$

Ka Hin Leung·Koji Momihara·Qing Xiang
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Abstract

Let $q$ be a prime power of the form $q=12c^2+4c+3$ with $c$ an arbitrary integer. In this paper we construct a difference family with parameters $(2q^2;q^2,q^2,q^2,q^2-1;2q^2-2)$ in ${\mathbb Z}_2\times ({\mathbb F}_{q^2},+)$. As a consequence, by applying the Wallis-Whiteman array, we obtain Hadamard matrices of order $4(2q^2+1)$ for the aforementioned $q$'s.

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Ka Hin Leung, Koji Momihara, Qing Xiang. 2019-07-04. A new family of Hadamard matrices of order $4(2q^2+1)$. https://arxiv.org/abs/1907.02623

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