State space realization of 2-D finite-dimensional behaviours
SIAM Journal on Control and Optimization
Gröbner bases over Galois rings with an application to decoding alternant codes
Journal of Symbolic Computation
Multidimensional Convolutional Codes
SIAM Journal on Discrete Mathematics
SIAM Journal on Control and Optimization
On behaviors and convolutional codes
IEEE Transactions on Information Theory - Part 1
System-theoretic properties of convolutional codes over rings
IEEE Transactions on Information Theory
Reed-Solomon list decoding from a system-theoretic perspective
IEEE Transactions on Information Theory
Cyclic codes and minimal strong Gröbner bases over a principal ideal ring
Finite Fields and Their Applications
Exact linear modeling with polynomial coefficients
Multidimensional Systems and Signal Processing
Exact linear modeling using Ore algebras
Journal of Symbolic Computation
Finite multidimensional behaviors
Multidimensional Systems and Signal Processing
| Hi-index | 0.03 |
Given a finite set of polynomial-exponential, multivariate, and vector-valued sequences, we show how the smallest linear shift-invariant set containing the data trajectories can be written as the solution set of a system of linear difference equations with constant coefficients. The resulting representation is known as the most powerful unfalsified model (MPUM) in behavioral systems theory. We address the case where the components of the given sequences take their values in a field, as well as the case where these values belong to a finite ring of the form $${{\mathbb{Z}}/m{\mathbb{Z}}}$$ for an integer m 1.