Abstract-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 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. 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 p are obtained.Index Terms-Convolutional codes over rings, direct sum decomposition of rings, proper convolutional codes, systematic convolutional codes.

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Abstract-The result of a search for the world's second Type II (doubly-even and self-dual) convolutional code is reported. A rate = 4 8, 16-state, time-invariant, convolutional code with free distance = 8 was found to be Type II. The initial part of its weight spectrum is better than that of the Golay convolutional code (GCC). Generator matrices and path weight enumerators for some other Type II convolutional codes are given. By the "wrap-around" technique tail-biting versions of (32 16 8) Type II block codes are constructed.