Dual code: Difference between revisions

Revision as of 18:36, 13 May 2010

Revision as of 01:13, 29 May 2010

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{{for|players of both rugby codes see|List of dual-code rugby internationals}}

In [[coding theory]], the '''dual code''' of a [[linear code]]

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==Self-dual codes==

A '''self-dual code''' is one which is its own dual. This implies that ''n'' is even and dim ''C'' = ''n''/2. If a self-dual code is such that each codeword's weight is a multiple of some constant <math>c > 1</math>, then it is of one of the following four types<ref>{{cite book | last=Conway | first=J.H. | authorlink=John Conway | coauthors=Sloane,N.J.A. | authorlink2=Neil Sloane | title=Sphere packings, lattices and groups | series=Grundlehren der mathematischen Wissenschaften | volume=290 | publisher=[[Springer-Verlag]] | date=1988 | isbn=0-387-96617-X | page=77}}</ref>:

*'''Type I''' codes are binary self-dual codes which are not [[doubly-even code|doubly-even]]. Type I codes are always [[even code|even]] (every codeword has even [[Hamming weight]]).