Quaternary Convolutional Codes from Linear Block Codes over Galois Rings

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 Z
₄
with 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.