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I would like to know if any progress has been made on Hadamard conjecture : There exists a Hadamard matrix of order $n=4k$ $\forall k \in \mathbb{N}$.

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The wikipedia article seems up to date. –  Chris Godsil Jan 8 '12 at 18:48
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Warwick de Launey's paper "On the Asymptotic Existence of Hadamard Matrices", arxiv.org/abs/1003.4001, may be of interest. –  Will Orrick Jan 8 '12 at 19:45
    
Thank you all for the replies. –  Serifo Blade Jan 9 '12 at 2:25

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