Some results on convolutional codes over rings

Abstract

Convolutional codes over rings were motivated from phase-modulated signals. Some structural properties of generator matrices of convolutional codes over rings have been studied. A condition for a convolutional code over a ring to be systematic is given and shown to be equivalent to the condition given by Massey and Mittelholzer (1989). Furthermore, the conditions of generator matrices over Z(p/sup e/) being catastrophic, basic, and minimal are considered, and the predictable degree property of polynomial generator matrices is considered.