# Distance matrices of subsets of the Hamming cube

@article{Doust2020DistanceMO, title={Distance matrices of subsets of the Hamming cube}, author={Ian Doust and G. Neil Robertson and Alan Stoneham and Anthony Weston}, journal={arXiv: Functional Analysis}, year={2020} }

Graham and Winkler derived a formula for the determinant of the distance matrix of a full-dimensional set of $n + 1$ points $\{ x_{0}, x_{1}, \ldots , x_{n} \}$ in the Hamming cube $H_{n} = ( \{ 0,1 \}^{n}, \ell_{1} )$. In this article we derive a formula for the determinant of the distance matrix $D$ of an arbitrary set of $m + 1$ points $\{ x_{0}, x_{1}, \ldots , x_{m} \}$ in $H_{n}$. It follows from this more general formula that $\det (D) \not= 0$ if and only if the vectors $x_{0}, x_{1… Expand

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