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Codes of types I, II, III, or IV exist only if the length ''n'' is a multiple of 2, 8, 4, or 2 respectively.
If a self-dual code has a generator matrix of the form <math>G=[I_k|A]</math>, then the dual code <math>C^\perp</math> has [[generator matrix]] <math>[-\bar{A}^T|I_k]</math>, where <math>I_k</math> is the <math>(n/2)\times (n/2)</math> identity matrix and <math>\bar{a}=a^q\in\mathbb{F}_q</math>.
==References==
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