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::call it Walsh code or Walsh family. They note that the "Walsh family can be interpreted as a subcode of the first-order Reed-Muller code". If you study these references, you will see that the definitions match the "Hadamard code" or the "punctured Hadamard code". Sorry I don't have a better answer, but I do believe that there should only be a single article on this object. [[User:Ylloh|ylloh]] ([[User talk:Ylloh|talk]]) 20:20, 21 February 2013 (UTC)
:::So the short answer to the question is ''No''. In future please wait for a consensus of informed editors before following your own [[WP:OR|personal research]]. [[User:Deltahedron|Deltahedron]] ([[User talk:Deltahedron|talk]]) 22:40, 21 February 2013 (UTC)
::::This is not original research. I posted informed and relevant sources above and added them to the article itself. The routine change-of-notation that I used falls under [[Wikipedia:Scientific citation guidelines#Examples, derivations and restatements]] and is necessary to bring the material from different fields and different authors together. [[User:Ylloh|ylloh]] ([[User talk:Ylloh|talk]]) 04:31, 22 February 2013 (UTC)
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:::One thing one must be careful of is that the word "code" has a different meaning in the wireless communication literature than it does in the mathematics and computer science literature. Where the wireless communication literature says "code", the mathematics literature says "codeword"; in mathematics, a code is a set of codewords. By my reading, the quote above is saying that the Walsh and Hadamard codes (in the sense of mathematics) consist of the same codewords, but that the codewords are ordered differently. This bears further investigation: in particular, I have not found where "Hadamad code" is defined in the reference above [[User:Will Orrick|Will Orrick]] ([[User talk:Will Orrick|talk]]) 02:37, 22 February 2013 (UTC)
::::Yes, some people call codewords "codes". Thanks for the reference to Du & Swamy! I agree that they probably mean to say that the codewords are the same, but that the encoding function is different. [[User:Ylloh|ylloh]] ([[User talk:Ylloh|talk]]) 04:31, 22 February 2013 (UTC)
== "Punctured" Hadamard code ==
inner product code
In the literature, when the punctured Hadamard code is used, it is just called Hadamard code (or Walsh code). For the purposes of this article, I chose to use the term punctured Hadamard code to distinguish between the two variants of the Hadamard code. Another name would be "restricted Hadamard code" or "affine Hadamard code". An entirely different possibility would be to use a descriptive name for the purposes of this articel. The Hadamard code would be the "inner product code" (it corresponds to applying all linear functions in ''k'' variables to the message) and the punctured Hadamard code would be the "affine inner product code" (because it corresponds to applying an ''affine'' linear function in ''k'' variables to the message). [[User:Ylloh|ylloh]] ([[User talk:Ylloh|talk]]) 04:31, 22 February 2013 (UTC)
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