Paper Info
Title
The probability of primeness for specially structured polynomial matrices over finite fields with applications to linear systems and convolutional codes.
Abstract
We calculate the probability that random polynomial matrices over a finite field with certain structures are right prime or left prime, respectively. In particular, we give an asymptotic formula for the probability that finitely many non-singular polynomial matrices are mutually left coprime. These results are used to estimate the number of reachable and observable linear systems as well as the number of non-catastrophic convolutional codes. Moreover, we are able to achieve an asymptotic formula for the probability that a parallel connected linear system is reachable.
Year
DOI
Venue
2017
10.1007/s00498-017-0191-z
MCSS
Keywords
Field
DocType
Polynomial matrices,Finite fields,Linear systems,Reachability,Parallel connection,Convolutional codes
Discrete mathematics,Asymptotic formula,Finite field,Convolutional code,Linear system,Polynomial,Matrix (mathematics),Matrix polynomial,Coprime integers,Mathematics
Journal
Volume
Issue
ISSN
29
2
Math. Control Signals Syst. 29:8 (2017)
Citations 
PageRank 
References 
0
0.34
4
Authors
1
Name
Order
Citations
PageRank
Julia Lieb121.50