Complex Hadamard matrices and Equiangular Tight Frames
Ferenc Sz\"oll\H{o}si
TL;DR
This paper introduces a new method for constructing parametric complex Hadamard matrices and links them to equiangular tight frames, expanding the known examples and including a novel (36,21) frame.
Contribution
It presents a novel construction of parametric complex Hadamard matrices and extends the catalog of equiangular tight frames, including the first (36,21) example from a cube root signature matrix.
Findings
New parametric families of complex Hadamard matrices are constructed.
Extended list of known equiangular tight frames.
First (36,21) frame derived from a cube root signature matrix.
Abstract
In this paper we give a new construction of parametric families of complex Hadamard matrices of square orders, and connect them to equiangular tight frames. The results presented here generalize some of the recent ideas of Bodmann et al. and extend the list of known equiangular tight frames. In particular, a (36,21) frame coming from a nontrivial cube root signature matrix is obtained for the first time.
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