Binary linear code

The vector space $𝕂 𝑛 2$ is equivalent to the powerset $P (Ω 𝑛)$ where $Ω 𝑛$ is a set with $𝑛$ elements, and addition is given by symmetric difference. #m/def/code Thus a binary linear code $C$ is a $G F (2)$ -subspace of $P (Ω 𝑛)$ .¹ Indeed, the main advantage of this notation is that it allows the importing of notations from set theory.