Dual code

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

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

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

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