The construction of Maximum Distance Profile (MDP) convolutional codes in general requires the use of very large finite fields. In contrast convolutional codes with optimal column distances maximize the column distances for a given arbitrary finite field. In this paper, we present a construction of such convolutional codes. In addition, we prove that for the considered parameters the codes that we constructed are the only ones achieving optimal column distances. The structure of the presented convolutional codes with optimal column distances is strongly related to first order Reed-Muller block codes and we leverage this fact to develop a reduced complexity version of the Viterbi algorithm for these codes.

翻译：最大距离特性（MDP）卷积码的构造通常需要使用非常大的有限域。相比之下，具有最优列距离的卷积码在任意给定的有限域上最大化其列距离。本文提出了一种此类卷积码的构造方法。此外，我们证明了对于所考虑的参数，我们所构造的码是唯一能达到最优列距离的码。所提出的具有最优列距离的卷积码的结构与一阶Reed-Muller分组码密切相关，我们利用这一事实为这些码开发了一种降低复杂度的Viterbi算法版本。