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I know the way of multiplying using FFT which takes $O(dlgd)$. If you know something better please share. If you have some nontrivial method for general matrices (not circulant), then also please reply. Any suggestions related to this question will help.

Jagdeep
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  • It will be sufficent for me, if you can give a better way to multiply circulant matrix A$\in {0,1}^{d\times d}$ with vector x$\in \mathbb{R}^{d}$. – Jagdeep Sep 15 '14 at 13:38

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