Criteria for the construction of MDS convolutional codes with good column distances

Maximum-distance separable (MDS) convolutional codes are characterized by the property that their free distance reaches the generalized Singleton bound. In this paper, new criteria to construct MDS convolutional codes are presented. Additionally, the obtained convolutional codes have optimal first (reverse) column distances and the criteria allow to relate the construction of MDS convolutional codes to the construction of reverse superregular Toeplitz matrices. Moreover, we present some construction examples for small code parameters over small finite fields.