In order to develop a new theoretical basis for autonomous devices of molecular electronics, a model of topological coding of chain polymers is proposed. The model is based on the property of the main chain of polymers to form a helix due to conjugated ionic-hydrogen-bond systems (connectivity). It includes the topological code, the algorithm of coding, and the system of physical operators for reconstruction of the encoded structure. The basic principle of the approach consists of the analogy between a 4-link fragment of a polymer and 4-arc graph. It was found that 64 connectivity states (conformations) of the graph can be described in the binary system by matrices of 6 variables that form a supermatrix containing 4 blocks. Using the 4-letter alphabet, matrices and the supermatrix are converted into triplets and the topological code. An algorithm suitable for computer programming is proposed for coding the n-arc graph and polymer chain. Physical operators were shown either to enhance or suppress the spontaneous capacity of polymers to form helices. Physical operators are assigned to the triplets of the topological code. From the viewpoint of the model, only proteins, nucleic acids, and their close analogs are recognized as prospective materials of future devices for molecular electronics.