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Maximum-distance separable (MDS) convolutional codes are characterized by theproperty that their free distance reaches the generalized Singleton bound. Inthis 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 MDSconvolutional codes to the construction of reverse superregular Toeplitzmatrices. Moreover, we present some construction examples for small codeparameters over small finite fields.

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