Constant-weight code: Difference between revisions

Revision as of 21:27, 2 September 2009

Revision as of 13:45, 25 January 2010

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{{Mergefrom|M of n codes|discuss=Talk:M of n codes|date=April 2008}}

In [[coding theory]], a '''constant-weight code''', also called an '''m of n code''', is an [[error detection and correction]] code where all codewords share the same [[Hamming weight]]. The theory is closely connected to that of [[Combinatorial design|designs]] (such as [[block design|''t''-design]]s and [[Steiner system]]s) and has several applications, including [[Frequency-hopping spread spectrum|frequency hopping]] in [[Global System for Mobile Communications|GSM]] networks.<ref name="smith">D. H. Smith, L. A. Hughes and S. Perkins (2006). "[http://www.combinatorics.org/Volume_13/Abstracts/v13i1a2.html A New Table of Constant Weight Codes of Length Greater than 28]". ''The Electronic Journal of Combinatorics'' '''13'''.</ref> Most of the work on this very vital field of [[discrete mathematics]] is concerned with ''binary'' constant-weight codes. In addition to use as error correction codes, the large space between code words can also be used in the design of [[asynchronous andcircuit]]s such as [[delay insensitive circuits,circuit]]s.

== ''A''(''n'',''d'',''w'') ==

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== 1 of N codes ==

{{main|one-hot}}

A special case of constant weight codes are the one-of-N codes, that encode <math>log_2 N</math> bits in a code-word of <math>N</math> bits. The one-of-two code uses the code words 01 and 10 to encode the bits '0' and '1'. a one-of-four code can use the words 0001, 0010, 0100, 1000 in order to encode two bits 00, 01, 10, and 11. An example is [[dual rail encoding]], and chain link <ref>{{cite article

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| url=http://www.silistix.com/members/privatePapers/designwave2.pdf

| coauthors=W.J.Bainbridge, A.Bardsley, R.W.McGuffin

}}</ref>used in [[Delay insensitive circuit|delay insensitive circuits]].

== References ==