Convolutional codes over rings have been motivated by phase-modulated signals. Some structural properties of the generator matrices of such codes are presented. Successively stronger notions of the invertibility of generator matrices are studied, and a new condition for a convolutional code over a ring to be systematic is given and shown to be equivalent to a condition given by Massey and Mittelholzer (1990). It is shown that a generator matrix that can be decomposed into a direct sum is basic, minimal, and noncatastrophic if and only if all generator matrices for the constituent codes are basic, minimal, and noncatastrophic, respectively. It is also shown that if a systematic generator matrix can be decomposed into a direct sum, then all generator matrices of the constituent codes are systematic, but that the converse does not hold. Some results on convolutional codes over Z(p/sup e/) are obtained.
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机译：环上的卷积码是由调相信号驱动的。给出了这种代码的生成器矩阵的一些结构特性。研究了生成器矩阵可逆性的逐步更强的概念，并给出了环上卷积码成为系统的新条件，并证明该条件等同于Massey和Mittelholzer（1990）给出的条件。结果表明，当且仅当构成代码的所有生成矩阵分别是基本，最小和非灾难性时，可以分解为直接和的生成器矩阵才是基本，最小和非灾难性的。还表明，如果可以将系统的生成器矩阵分解为直接和，则构成代码的所有生成器矩阵都是系统的，但是反之则不成立。获得了关于Z（p / sup e /）上的卷积码的一些结果。
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