Pairing of Finite Modules, Duality of Linear Codes, and the MacWilliams Identities

The concept of the duality of codes well known in coding theory is introduced for submodules of a pair of finite modules related by a ertain binary bilinear relation. Therewith, a air of antiisomorphic complete lattices of dual submodules arises. Under certain conditions, the MacWilliams identities which connect the characteristics of a pair of mutually dual codes are proved.