Counting Polynomial Matrices over Finite Fields

Counting Polynomial Matrices over Finite Fields

Matrices with Certain Primeness Properties and Applications to Linear Systems and Coding Theory

Julia Lieb

Paperback

164 Seiten

ISBN-13: 9783958260641

Verlag: Würzburg University Press

Erscheinungsdatum: 15.09.2017

Sprache: Englisch

Farbe: Nein

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This book is dealing with three mathematical areas, namely polynomial matrices over finite fields, linear systems and coding theory.
Primeness properties of polynomial matrices provide criteria for the reachability and observability of interconnected linear systems. Since time-discrete linear systems over finite fields and convolutional codes are basically the same objects, these results could be transferred to criteria for non-catastrophicity of convolutional codes.
In particular, formulas for the number of pairwise coprime polynomials and for the number of mutually left coprime polynomial matrices are calculated. This leads to the probability that a parallel connected linear system is reachable and that a parallel connected convolutional code is non-catastrophic. Moreover, other networks of linear systems and convolutional codes are considered.
Julia Lieb

Julia Lieb

Geboren 1988 in Kronach, M.Sc. (Mathematik), Studium der Fächer Mathematik, Katholische Theologie und Erziehungswissenschaften (Staatsexamen)

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