Abstract:A Hadamard matrix is balanced splittable if some subset of its rows has the property that the dot product of every two distinct columns takes at most two values. This definition was introduced by Kharaghani and Suda in 2019, although equivalent formulations have been previously studied using different terminology. We collate previous results phrased in terms of balanced splittable Hadamard matrices, real flat equiangular tight frames, spherical two-distance sets, and two-distance tight frames. We use combinato… Show more
“…Balancedly splittable Hadamard matrices were introduced by the authors in 2018 in [8], and the results were widely expanded in a recent paper by Jonathan Jedwab et al in [5]. It is known [7] that the existence of a Hadamard matrix of order 4n would lead to a balancedly splittable Hadamard matrix of order 64n 2 .…”
Let $n$ be the order of a quaternary Hadamard matrix. It is shown that the existence of a projective plane of order $n$ is equivalent to the existence of a balancedly multi-splittable quaternary Hadamard matrix of order $n^2$.
“…Balancedly splittable Hadamard matrices were introduced by the authors in 2018 in [8], and the results were widely expanded in a recent paper by Jonathan Jedwab et al in [5]. It is known [7] that the existence of a Hadamard matrix of order 4n would lead to a balancedly splittable Hadamard matrix of order 64n 2 .…”
Let $n$ be the order of a quaternary Hadamard matrix. It is shown that the existence of a projective plane of order $n$ is equivalent to the existence of a balancedly multi-splittable quaternary Hadamard matrix of order $n^2$.
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