Convolutional codes over rings and the two chain conditions

Convolutional codes over rings were proposed as appropriate codes for phase modulation (Baldini Filho et al., 1987, Baldini, Filho and Farrell, 1990, and Massey and Mittelholzer, 1989). Structural properties of ring codes were considered in Massey and Mittelholzer (1990) and Johannesson et al. Convolutional codes over rings can have surprisingly different properties from codes over fields; these differences depend strongly on the structure of the underlying ring. In this paper, some simple basic properties of ring codes are considered and related to two well-known chain conditions that can be imposed on a ring (Atiyah, 1969)