Maximum distance separable (MDS) block codes and MDS 1D convolutional codes are the most robust codes for error correction within the class of block codes of a fixed rate and 1D convolutional codes of a certain rate and degree, respectively. In this paper, we generalize this concept to the class of 2D convolutional codes. For that, we introduce a natural bound on the distance of a 2D convolutional code of rate    $k/n$    and degree    $\delta $   , which generalizes the Singleton bound for block codes and the generalized Singleton bound for 1D convolutional codes. Then, we prove the existence of 2D convolutional codes of rate    $k/n$    and degree    $\delta $    that reach such bound when    $n \geq k (({(\lfloor ({\delta }/{k}) \rfloor + 2)(\lfloor ({\delta }/{k}) \rfloor + 3)})/{2})$    if    $k {\nmid } \delta $   , or    $n \geq k (({(({\delta }/{k}) + 1)(({\delta }/{k}) + 2)})/{2})$    if    $k \mid \delta $   , by presenting a concrete constructive procedure.
['Joan-Josep Climent', 'Diego Napp', 'Carmen Perea', 'Raquel Pinto']
Maximum Distance Separable 2D Convolutional Codes