Dual code: Difference between revisions

Revision as of 22:57, 9 May 2005

Revision as of 00:19, 10 May 2005

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Communication Theory. The <i>'''dual</i>''' of a [[linear code]] <math>C\subset\mathbb{F}_2^n</math> is defined to be

<math>C^\perp = \{x \in \mathbb{F}_2^n \mid <x,c> = 0 \forall c \in C \} </math>

where <,> denotes the vector [[dot product]] (which is taken over the [[field (mathematics)|field]] <math>\mathbb{F}_2</math>).

An important property is that the dual of the dual code is the original code itself.

{{technical}}