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:<math>\dim C + \dim C^\perp = n.</math>
A [[generator matrix]] for the dual code is
==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 Horton Conway | author2=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=[https://archive.org/details/spherepackingsla0000conw/page/77 77] | url=https://archive.org/details/spherepackingsla0000conw/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]]).
*'''Type II''' codes are binary self-dual codes which are doubly even.
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