Dual of a linear code

Definition
The dual of a linear code $$(V,X,W)$$ is defined as the linear code $$(V,X,W')$$ where $$W'$$ 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.