Block codes are often described using one of these structures over GF(2). A prominent example of acontravariant functor is the duality on the category of these structures. A generalization of these structuresis defined over a ring and is a module. A subset of these structures is the subject of the Steinitz exchangelemma. Over a field F, they can be defined as an abelian group, A, and a ring homomorphism from F to theendom
Block codes are often described using one of these structures over GF(2). A prominent example of acontravariant functor is the duality on the category of these structures. A generalization of these structuresis defined over a ring and is a module. A subset of these structures is the subject of the Steinitz exchangelemma. Over a field F, they can be defined as an abelian group, A, and a ring homomorphism from F to theendomorphism ring of A, which maps the identity to the identity. One property of these structures can befound by adding the dimension of the image and kernel of a linear transformation according to therank-nullity theorem. These structures are closed under addition and scalar multiplication. For 10 points,identify these spaces studied in linear algebra.
Block codes are often described using one of these structures over GF(2).
vector spaces [or vector spaces after "spaces" is read]