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Block companion Singer cycles, primitive recursive vector sequences, and coprime polynomial pairs over finite fields

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Title Block companion Singer cycles, primitive recursive vector sequences, and coprime polynomial pairs over finite fields
 
Creator GHORPADE, SR
RAM, S
 
Subject FEEDBACK SHIFT REGISTERS
FACTORIZATION
Singer cycle
Block companion matrix
Multiple recursive matrix method
Linear feedback shift register (LFSR)
Splitting subspace
Toeplitz matrix
 
Description We discuss a conjecture concerning the enumeration of nonsingular matrices over a finite field that are block companion and whose order is the maximum possible in the corresponding general linear group. A special case is proved using some recent results on the probability that a pair of polynomials with coefficients in a finite field is coprime. Connection with an older problem of Niederreiter about the number of splitting subspaces of a given dimension are outlined and an asymptotic version of the conjectural formula is established. Some applications to the enumeration of nonsingular Toeplitz matrices of a given size over a finite field are also discussed. (C) 2011 Elsevier Inc. All rights reserved.
 
Publisher ACADEMIC PRESS INC ELSEVIER SCIENCE
 
Date 2012-06-26T06:44:24Z
2012-06-26T06:44:24Z
2011
 
Type Article
 
Identifier FINITE FIELDS AND THEIR APPLICATIONS,17(5)461-472
1071-5797
http://dx.doi.org/10.1016/j.ffa.2011.02.008
http://dspace.library.iitb.ac.in/jspui/handle/100/14069
 
Language English