Maximum distance separable convolutional codes are characterized by the property that the free distance reaches the generalized Singleton bound, which makes them optimal for error correction. However, the existing constructions of such codes are available over fields of large size. In this paper, we present the unique construction of MDS convolutional codes of rate $1/2$ and degree $5$ over the field $\mathbb{F}_{11}$.

翻译：最大距离可分卷积码具有自由距离达到广义Singleton界的特性，这使得它们在纠错方面达到最优。然而，现有此类码的构造通常需要大尺寸的域。本文提出了一种在域$\mathbb{F}_{11}$上构造速率为$1/2$、度为$5$的MDS卷积码的独特方法。