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I corrected one serious error on this page. Someone should carefully check this and fix the others. —Preceding unsigned comment added by 71.179.164.101 ( talk • contribs) 15:08, 9 March 2008
The two articles were nearly identical and have now been merged. For this, I streamlined the definitions and moved the local decodability section to Hadamard code. The merger has been previously discussed here. Note that the article Walsh–Hadamard code originated from the article Walsh code, which is the name that seems to be used for this code in telecommunications / engineering. It would be good if someone could expand the article from that perspective a bit. ylloh ( talk) 19:12, 21 February 2013 (UTC)
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 article. 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). ylloh ( talk) 04:31, 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 [2] 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. — Preceding unsigned comment added by Hpfister ( talk • contribs) 15:48, 15 September 2019 (UTC)
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The nondegenerate bilinear form defined in the article is not an inner product. Taking x = 1 yields a counterexample to the positive definiteness. — Preceding unsigned comment added by Ntheazk ( talk • contribs) 16:37, 20 March 2020 (UTC)
This article is rated C-class on Wikipedia's
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I corrected one serious error on this page. Someone should carefully check this and fix the others. —Preceding unsigned comment added by 71.179.164.101 ( talk • contribs) 15:08, 9 March 2008
The two articles were nearly identical and have now been merged. For this, I streamlined the definitions and moved the local decodability section to Hadamard code. The merger has been previously discussed here. Note that the article Walsh–Hadamard code originated from the article Walsh code, which is the name that seems to be used for this code in telecommunications / engineering. It would be good if someone could expand the article from that perspective a bit. ylloh ( talk) 19:12, 21 February 2013 (UTC)
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 article. 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). ylloh ( talk) 04:31, 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 [2] 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. — Preceding unsigned comment added by Hpfister ( talk • contribs) 15:48, 15 September 2019 (UTC)
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I have just modified one external link on Hadamard code. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
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Cheers.— InternetArchiveBot ( Report bug) 19:21, 27 October 2017 (UTC)
The nondegenerate bilinear form defined in the article is not an inner product. Taking x = 1 yields a counterexample to the positive definiteness. — Preceding unsigned comment added by Ntheazk ( talk • contribs) 16:37, 20 March 2020 (UTC)