Constant-weight code: Difference between revisions

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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). andMost of the work on this very vital field of [[discrete mathematics]] is concerned with ''binary'' constant-weight codes.

Binary constant-weight codes hashave 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 mathematicsbarcode]]s isuse concerneda with ''binary'' constant-weight codescode to simplify automatically setting the threshold.
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.

Constant-weight codes, like [[Berger code]]s, can detect all unidirectional errors.

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