Quaternary Convolutional Codes From Linear Block Codes Over Galois Rings

摘要

From a linear block code $B$ over the Galois ring ${hbox{GR}}(4,m)$ with a $ktimes n$ generator matrix and minimum Hamming distance $d$, a rate- $k$ convolutional code over the ring $ {BBZ }_{4}$ with 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–Varshamov bound.