Counting Polynomial Matrices over Finite Fields : Matrices with Certain Primeness Properties and Applications to Linear Systems and Coding Theory

Julia Lieb

ISBN 10: 3958260640 / ISBN 13: 9783958260641

Published by Würzburg University Press, 2017

About this Item

nach der Bestellung gedruckt Neuware - Printed after ordering - 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.

Seller Inventory # 9783958260641

Bibliographic Details

• Title: Counting Polynomial Matrices over Finite Fields : Matrices with Certain Primeness Properties and Applications to Linear Systems and Coding Theory
• Publisher: Würzburg University Press
• Publication Date: 2017
• Language: English
• ISBN 10: 3958260640
• ISBN 13: 9783958260641
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 240W x 170H x 11D millimeters 240 millimeters width by 170 millimeters height by 11 millimeters depth
• Weight: 324 grams

About this title

Synopsis

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.