Dual of a linear code

Definition

The dual of a linear code $(V,X,W)$ is defined as the linear code $(V,X,W^{\prime })$ where $W^{\prime }$ is the orthogonal complement of $W$ with respect to the standard inner product defined by the basis $X$.

In the case of a binary linear code, it is the set of those subsets which intersect every set in the space of code-words, in a subset of even cardinality.