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::As far as I am aware, some authors use “Hadamard code” to refer to this more general construction, which doesn't even require that the Hadamard matrix have power-of-two order.[[User:Will Orrick|Will Orrick]] ([[User talk:Will Orrick|talk]]) 04:04, 15 March 2008 (UTC)
:::If the code is constructed as the rows of <math>\begin{bmatrix}H & -H\end{bmatrix}^T</math>, then there are 2<sup>''N''+1</sup> codes. Therefore, they can be described by an (''N''+1)-bit index. Therefore the code will be (2<sup>''N''</sup>, ''N''+1). How do you get (2<sup>''N''</sup>, 2<sup>''N''+1</sup>)? In fact, that doesn't even make sense; in an (''n'',''k'') code, ''n'' cannot be less than ''k'', otherwise you would be achieving perfect compression!
:::I'm no expert on Hadamard matrices; by "there are millions of Hadamard matrices of order 32", are you implying that there are order-32 Hadamard matrices that cannot be derived from Sylvester's construction by simple row/column permutation? If so, we do indeed need to clarify that the code is based on matrices from Sylvester's construction. [[User:Oli Filth|Oli Filth]]<sup>([[User talk:Oli Filth|talk]])</sup> 15:41, 15 March 2008 (UTC)
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