Systematic Unit-Memory Binary Convolutional Codes from Linear Block Codes over F2r + vF2r

Two constructions of unit-memory binary convolutional codes from linear block codes over the finite semi-local ring F2r + vF2r , where v = v, are presented. In both cases, if the linear block code is systematic, then the resulting convolutional encoder is systematic, minimal, basic and non-catastrophic. The Hamming free distance of the convolutional code is bounded below by the minimum Hamming distance of the block code. New examples of binary convolutional codes that meet the Heller upper bound for systematic codes are given. Keywords—Convolutional codes, semi-local ring, free distance, Heller bound.