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{{short description|Method for encoding data in communications}}
{{Use dmy dates|date=May 2019|cs1-dates=y}}
In [[coding theory]], a '''constant-weight code''', also called an '''''m''-of-''n'' code''' or '''''m''-out-of-''n'' code''', is an [[error detection and correction]] code where all codewords share the same [[Hamming weight]].
The [[one-hot]] code and the '''balanced code''' are two widely used kinds 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
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>
Most [[barcode]]s use a binary constant-weight code to simplify automatically setting the brightness threshold that distinguishes black and white stripes.
Most [[line code]]s use either a constant-weight code, or a nearly-constant-weight [[paired disparity code]].
In addition to use as error correction codes, the large space between code words can also be used in the design of [[asynchronous circuit]]s such as [[delay insensitive circuit]]s.
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|title=Very efficient balanced codes
|author=[[Kees Schouhamer Immink|K. Schouhamer Immink]] and J. Weber
|issue=2
|url=https://www.researchgate.net/publication/
|pages=188–192
|accessdate=2018-02-12
|doi=10.1109/jsac.2010.100207
|s2cid=8596702
}}</ref>
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[[biphase mark code]] uses a 1 of 2 code;
[[6b/8b encoding]] uses a 4 of 8 code;
the [[Hadamard code]] is a <math>2^{k
the [[IEEE 1355#Slice: TS-FO-02|three-of-six]] code;
etc.
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== External links ==
* [http://www.win.tue.nl/~aeb/codes/Andw.html Table of lower bounds on <math>A(n,d,w)</math>] maintained by [[Andries Brouwer]]
* [http://codes.se/bounds/ Table of upper bounds on <math>A(n,d,w)</math>] maintained by [[Erik Agrell]]
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