The predictable degree property and row reducedness for systems over a finite ring

DOI10.1016/j.laa.2007.04.015zbMath1127.93038OpenAlexW2170421451MaRDI QIDQ998209

Jan Willem Polderman, Raquel Pinto, Margreta Kuijper

Publication date: 27 August 2007

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2007.04.015

zbMATH Keywords

linear systemsparametrizationpolynomial matriceskernel representationsannihilatorsfinite ringsbehaviorspredictable degree propertyrow reduced

Mathematics Subject Classification ID

Discrete-time control/observation systems (93C55) Linear systems in control theory (93C05) System structure simplification (93B11) Algebraic methods (93B25)

Related Items

The Dual of Convolutional Codes Over $${\mathbb {Z}}_{p^r}$$, Bilinear forms graphs over residue class rings, List decoding of convolutional codes over integer residue rings, State representations of convolutional codes over a finite ring, Minimal Gröbner bases and the predictable leading monomial property, Finite multidimensional behaviors, Convolutional codes over finite chain rings, MDP codes and their characterization, Minimal Trellis Construction for Finite Support Convolutional Ring Codes, On MDS convolutional codes over \(\mathbb{Z}_{p^r}\), An iterative algorithm for parametrization of shortest length linear shift registers over finite chain rings, Noncatastrophic convolutional codes over a finite ring

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• From time series to linear system. I: Finite dimensional linear time invariant systems
• From time series to linear system, II. Exact modelling
• Canonical kernel representations for behaviors over finite Abelian groups
• Fast projection methods for minimal design problems in linear system theory
• Linear multivariable systems
• On minimal realization over a finite chain ring
• Modular and \(p\)-adic cyclic codes
• Generalized GMW quadriphase sequences satisfying the Elch bound with equality
• An efficient algorithm for constructing minimal trellises for codes over finite abelian groups
• Minimal Bases of Rational Vector Spaces, with Applications to Multivariable Linear Systems
• Reed–Solomon List Decoding From a System-Theoretic Perspective
• LDPC Codes Over Rings for PSK Modulation
• Paradigms and puzzles in the theory of dynamical systems
• 4-phase sequences with near-optimum correlation properties
• The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes
• Some structural properties of convolutional codes over rings
• System-theoretic properties of convolutional codes over rings