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.

翻译：最大距离可分（MDS）卷积码以其自由距离达到广义Singleton界为特征。本文提出了构造MDS卷积码的新准则。此外，所获得的卷积码具有最优的第一（反向）列距离，且这些准则将MDS卷积码的构造与反向超正则Toeplitz矩阵的构造联系起来。同时，我们给出了有限域上小码参数的部分构造实例。