Talk:Hadamard code: Difference between revisions

Revision as of 15:29, 22 February 2013

Latest revision as of 01:08, 9 March 2024

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== Old discussion ==

I corrected one serious error on this page. Someone should carefully check this and fix the others. <small>—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:71.179.164.101|71.179.164.101]] ([[User talk:71.179.164.101|talk]] • [[Special:Contributions/71.179.164.101|contribs]]) 15:08, 9 March 2008</small><!-- Template:Unsigned -->

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::::::I've been watching this page for a long time, and I just don't see that there is a large body of "informed editors" prepared to weigh in and resolve the discrepancies between different sources. I'm grateful that Ylloh has taken on the onerous task of describing the competing conventions and definitions that appear in the literature. I see no problem with the edits that have been made so far.[[User:Will Orrick|Will Orrick]] ([[User talk:Will Orrick|talk]]) 12:07, 22 February 2013 (UTC)

* I added a merger template to [[Walsh–Hadamard code]]. If there's no substantial opposition in the next few weeks, I suggest that the merger is completed (by replacing [[Walsh–Hadamard code]] with a redirect; the content has already been merged into [[Hadamard code]]). [[User:Ylloh|ylloh]] ([[User talk:Ylloh|talk]]) 18:04, 25 February 2013 (UTC)

== "Punctured" Hadamard code ==

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::That's exactly why I'm trying to ask for a discussion here. I handled the situation the way I did, and I'm interested in whether other editors have better ideas. [[User:Ylloh|ylloh]] ([[User talk:Ylloh|talk]]) 15:29, 22 February 2013 (UTC)

First, I want to acknowledge Ylloh for significantly improving this page. Second, I want to note that I am professor in ECE and teach graduate classes on this subject. I was drawn to this page because a student in my class was incorrectly using the term "punctured Hadamard code" based on this Wikipedia page. The "punctured Hadamard code" is a [2^k - 1, k,2^{k-1} - 1] code formed by puncturing any single bit of the Hadamard code (all are equivalent). This family is dual to the family of [2^k - 1,2^k - k - 1,3] Hamming codes, up to equivalence. For example, this reference [http://pages.cs.wisc.edu/~dieter/Courses/2013s-CS880/Scribes/PDF/lecture03.pdf] makes this point without discussing equivalence). I don't know if there is a standard term (other than 1st-order Reed-Muller) for the code this page calls the "punctured Hadamard code". Using standard terminology, however, it should be called the "augmented Hadamard code" because augmenting refers to increasing the dimension by one whereas puncturing refers to reducing the length by 1. Thus, I am going fix this on the main page. <!-- Template:Unsigned --><small class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Hpfister|Hpfister]] ([[User talk:Hpfister#top|talk]] • [[Special:Contributions/Hpfister|contribs]]) 15:48, 15 September 2019 (UTC)</small> <!--Autosigned by SineBot-->

== External links modified ==

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I have just modified one external link on [[Hadamard code]]. Please take a moment to review [https://en.wikipedia.org/w/index.php?diff=prev&oldid=807408345 my edit]. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit [[User:Cyberpower678/FaQs#InternetArchiveBot|this simple FaQ]] for additional information. I made the following changes:

*Added archive https://web.archive.org/web/20110720084646/http://www.complextoreal.com/CDMA.pdf to http://www.complextoreal.com/CDMA.pdf

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== Not an inner product ==

The nondegenerate bilinear form defined in the article is not an inner product. Taking x = 1 yields a counterexample to the positive definiteness. <!-- Template:Unsigned --><small class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Ntheazk|Ntheazk]] ([[User talk:Ntheazk#top|talk]] • [[Special:Contributions/Ntheazk|contribs]]) 16:37, 20 March 2020 (UTC)</small> <!--Autosigned by SineBot-->