Binary linear code
A binary linear code is a vector subspace of the power set of a finite set . Here, the power set of a finite set is treated as a vector space via the usual XOR operation.
Value taken for terms from general theory of linear codes
This is the dimension of the vector subspace.
This is the size of the set .
Weight of the code
This is simply the minimum cardinality among all members of (note that each member of is a subset of so it makes sense to talk of its cardinality).