Talk:Hadamard code: Difference between revisions

Revision as of 19:40, 21 February 2013

Revision as of 20:20, 21 February 2013

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:Is there a [[WP:RS|reliable source]] that discusses the relationship between these terms? [[User:Deltahedron|Deltahedron]] ([[User talk:Deltahedron|talk]]) 19:40, 21 February 2013 (UTC)

::The problem is that sources from different fields and even sources within the same field call this object differently, and I did not find a single source that points out that there are different names. For example,

::* {{Citation

| last1=Arora | first1=Sanjeev | authorlink1=Sanjeev Arora

| last2=Barak | first2=Boaz

| title=Computational Complexity: A Modern Approach

| url = http://www.cs.princeton.edu/theory/complexity/

| publisher=[[Cambridge University Press|Cambridge]]

| year=2009

| isbn=978-0-521-42426-4

| zbl=1193.68112

}}

::call it the Walsh-Hadamard code.

::* Guruswami, Venkatesan. "List decoding of binary codes." [[http://www.cs.cmu.edu/~venkatg/pubs/papers/ld-binary-ms.pdf]]

::calls it Hadamard code, and notes "The order 1 RM [ [[Reed–Muller code|Reed–Muller]] ] code corresponds to evaluations of linear polynomials on <math>\mathbb F_2^m</math> and is often called the Hadamard code" (furthermore, he points out in a footnote: "To be accurate, the Hadamard code only encodes linear polynomials with no constant term but this is a minor difference.", which means he's referring to the Hadamard code and not the "punctured" Hadamard code).

::* {{Citation

| last1=Amadei | first1=M.

| last2=Manzoli | first2=U.

| last3=Merani | first3=M.L.

| title=On the assignment of Walsh and quasi-orthogonal codes in a multicarrier DS-CDMA system with multiple classes of users

| publisher=[[Cambridge University Press|Cambridge]]

| year=2002

| pages=841–845

| booktitle=Global Telecommunications Conference, 2002. GLOBECOM'02. IEEE

| volume=1

}}

::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)