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arXiv · 1701.08871

Circulant q-Butson Hadamard matrices

Trevor Hyde·Joseph Kraisler
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Abstract

If $q = p^n$ is a prime power, then a $d$-dimensional \emph{$q$-Butson Hadamard matrix} $H$ is a $d\times d$ matrix with all entries $q$th roots of unity such that $HH^* = dI_d$. We use algebraic number theory to prove a strong constraint on the dimension of a circulant $q$-Butson Hadamard matrix when $d = p^m$ and then explicitly construct a family of examples in all possible dimensions. These results relate to the long-standing circulant Hadamard matrix conjecture in combinatorics.

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Trevor Hyde, Joseph Kraisler. 2017-03-15. Circulant q-Butson Hadamard matrices. https://arxiv.org/abs/1701.08871

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