RT info:eu-repo/semantics/doctoralThesis
T1 Feedback Classification of linear systems and convolutional codes. Applications in cybernetics, coding theory and cryptography = Feedback clasificación de sistemas y códigos de convolución. Aplicaciones en cibernética, teoría de códigos y criptografía
A1 Castro-García, Noemí de
A2 Algebra
K1 Matemáticas
K1 Sistemas dinámicos lineales
K1 Códigos convolucionales
K1 Equivalencia feedback
AB Several natural phenomena are mathematically modeled through linear systems of differential equations. We study the feedback classification of linear systems over commutative rings with identity. In particular, we characterize von Neumann regular rings in terms of linear systems. Moreover, we give an explicit formula to give the number of classes of feedback isomorphisms of locally Brunovsky linear systems with state space X over different commutative rings by partitions in a monoid.Furthermore, we show that we can explicit interconnections between control theory and coding over certain commutative rings by generalizing the duality that exists over finite fields. We also study equivalence relations between certain families of convolutional codes and its I/S/O representations by their Kronecker Indices and their conjugate partitions. This final result is given by the correspondences between classes of feedback isomorphisms of locally Brunovsky linear system and classes of feedback isomorphisms of dynamical behaviours of I/S/O representations of certain families of convolutional codes.Finally, we give an overview of some areas of research with which this work is related. Some of them are a field of future research and the other areas can be considered as a field of implementation and applications
YR 2016
FD 2016-03-15
LK http://hdl.handle.net/10612/5166
UL http://hdl.handle.net/10612/5166
NO 180 p.
DS BULERIA. Repositorio Institucional de la Universidad de León
RD 22-may-2022