On MDS convolutional codes over $${\mathbb {Z}}_{p^{r}}$$.

Maximum distance separable (MDS) convolutional codes are characterized through the property that the free distance meets the generalized Singleton bound. The existence of free MDS convolutional codes over $${\mathbb {Z}}_{p^{r}}$$ was recently discovered in Oued and Sole (IEEE Trans Inf Theory 59(11):7305-7313, 2013) via the Hensel lift of a cyclic code. In this paper we further investigate this important class of convolutional codes over $${\mathbb {Z}}_{p^{r}}$$ from a new perspective. We introduce the notions of p-standard form and r-optimal parameters to derive a novel upper bound of Singleton type on the free distance. Moreover, we present a constructive method for building general (non necessarily free) MDS convolutional codes over $${\mathbb {Z}}_{p^{r}}$$ for any given set of parameters. [ABSTRACT FROM AUTHOR]