A new construction of an MDS convolutional code of rate 1/2

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 $\mathbb{F}_{11}$.