Finite multidimensional behaviors

Authors:
Eva Zerz;Lisa Wagner
Affiliations:
Lehrstuhl D für Mathematik, RWTH Aachen University, Aachen, Germany 52062;Lehrstuhl D für Mathematik, RWTH Aachen University, Aachen, Germany 52062
Venue:
Multidimensional Systems and Signal Processing
Year:
2012

Citing 6
Cited 1

State space realization of 2-D finite-dimensional behaviours

SIAM Journal on Control and Optimization
Regular Article: Finite Dimensional Systems of Partial Differential or Difference Equations

Advances in Applied Mathematics
Linear Codes and Polylinear Recurrences over Finite Rings and Modules

AAECC-13 Proceedings of the 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Gröbner bases with coefficients in rings

Journal of Symbolic Computation
The discrete multidimensional MPUM

Multidimensional Systems and Signal Processing
System-theoretic properties of convolutional codes over rings

IEEE Transactions on Information Theory

Controllability and Extendibility of Continuous Multi-dimensional Behaviors

Multidimensional Systems and Signal Processing

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Abstract

We study finitely generated and finite systems defined by linear partial difference equations with constant coefficients in a Noetherian ring. The two notions coincide for finite rings, and we show that all finite systems exhibit certain periodicity properties. For the particular case of systems over the ring of integers modulo m 1, which is important in coding theory, a method is given for determining the number of trajectories, using Gröbner basis techniques.