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）卷积码的特性在于其自由距离达到广义Singleton界。本文提出了构造MDS卷积码的新准则。此外，所得到的卷积码具有最优的第一（反向）列距离，且这些准则使得MDS卷积码的构造可与反向超正则Toeplitz矩阵的构造相关联。同时，我们给出了一些小码参数在小有限域上的构造实例。