Duality Between Multidimensional Convolutional Codes and Systems
Heide Gluesing-Luerssen, Joachim Rosenthal, Paul A. Weiner · Systems & control · 2001
Multidimensional convolutional codes arise as a generalization of “classical” one-dimensional codes. We introduce in-dimensional convolutional codes of length n as submodules of D’2where D is the polynomial ring in m variables over a finite field. Besides their coding theoretic significance, they can also be regarded as the annihilating modules of systems of partial difference equations, the latter being studied in much detail in discrete-time multidimensional systems theory. We apply the duality theorem of Oberst [5] to this particular case and employ the duality to investigate certain first-order representations of one-dimensional convolutional codes.