Dual code

Communication Theory. The dual of a linear code $C\subset \mathbb {F} _{2}^{n}$ is defined to be

$C^{\perp }=\{x\in \mathbb {F} _{2}^{n}\mid <x,c>=0\forall c\in C\}$

where <,> denotes the vector dot product (which is taken over the field (mathematics) $\mathbb {F} _{2}$).

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