Constant-weight code: Difference between revisions

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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]].
A [[one-hot]] code or a '''balanced code''' is a widely-used kind of constant-weight code.

The theory is closely connected to that of [[Combinatorial design|designs]] (such as [[block design|''t''-design]]s and [[Steiner system]]s). Most of the work on this very vital field of [[discrete mathematics]] is concerned with ''binary'' constant-weight codes.

Binary constant-weight codes have 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>

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== Balanced code ==

{{mergeto|constant-weight code|date=April 2012}}

In [[coding theory]], a '''balanced code''' is a [[binary numeral system|binary]] [[forward error correction]] code for which each codeword contains an equal number of zero and one bits. Balanced codes have been introduced by [[Donald Knuth]];<ref name="knuth">{{cite journal|author=D.E. Knuth|title=Efficient balanced codes|journal=IEEE Transactions on Information Theory|volume=32|issue=1|pages=51–53|date=January 1986|doi=10.1109/TIT.1986.1057136|url=http://www.costasarrays.org/costasrefs/knuth86efficient.pdf}}</ref> they are a subset of so-called unordered codes, which are codes having the property that the positions of ones in a codeword are never a subset of the positions of the ones in another codeword. Like all unordered codes, balanced codes are suitable for the detection of all [[unidirectional error]]s in an encoded message. Balanced codes allow for particularly efficient decoding, which can be carried out in parallel.<ref name="knuth"/><ref name="optimal">{{cite journal|author1=Sulaiman Al-Bassam|author2=Bella Bose|title=On Balanced Codes|journal=IEEE Transactions on Information Theory|volume=36|issue=2|pages=406–408|date=March 1990|doi=10.1109/18.52490}}</ref>

==References==

{{Reflist}}

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[[Category:Error detection and correction]]

== m of n codes==

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== References ==

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{{reflist}}

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== External links ==

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[[Category:Information theory]]

[[Category:Error detection and correction]]

[[Category:Error detection and correction]]

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