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portada Counting Polynomial Matrices Over Finite Fields
Type
Physical Book
Publisher
Author
Year
2017
Language
English
Pages
164
Format
Paperback
ISBN13
9783958260641
Categories

Counting Polynomial Matrices Over Finite Fields

Julia Lieb (Author) · Würzburg University Press · Paperback

Counting Polynomial Matrices Over Finite Fields - Julia Lieb

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Synopsis "Counting Polynomial Matrices Over Finite Fields "

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.

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