In this paper, bounds are derived on the minimum homogeneous distance of the image of a linear block code over the Galois ring GR(pr,m), with respect to any basis of GR(pr, m). These bounds depend on the parameters of GR(pr, m), the minimum Hamming distance of the block code, and the average value of the homogeneous weight applied on the base ring Zpr. Examples are given of Galois ring codes that meet these bounds.

From a linear block code B over the Galois ring GR(4, to) with a k x n generator matrix and minimum Hamming distance d, a rate-k/n convolutional code over the ring Z4with squared Euclidean free distance at least 2d and a non-recursive encoder with memory at most to m-1 is constructed. When the generator matrix of B is systematic, the convolutional encoder is systematic, basic, non-catastrophic and minimal. Long codes constructed in this manner are shown to satisfy a Gilbert-Varshamov bound.

From a linear block code B over the Galois ring GR(4, m) with a k times n generator matrix and minimum Hamming distance d, a rate-k/n convolutional code over the ring Z4with squared Euclidean free distance at least 2d and a nonrecursive encoder with memory at most m - 1 is constructed. When the generator matrix of B is systematic, the convolutional encoder is systematic, basic, noncatastrophic and minimal. Long codes constructed in this manner are shown to satisfy a Gilbert-Varshnmov bound.

In this correspondence, bounds are derived on the minimum homogeneous distance of the image of a linear block code over the Galois ring${\hbox{GR}}(p^{r},m)$, with respect to any basis of${\hbox{GR}}(p^{r},m)$. These bounds depend on the parameters of${\hbox{GR}}(p^{r},m)$, the minimum Hamming distance of the block code, and the average value of the homogeneous weight applied on the base ring$ {\BBZ }_{p^{r}}$. Examples are given of Galois ring codes that meet these bounds.