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Please use this identifier to cite or link to this item: http://dspace.library.iitb.ac.in/jspui/handle/100/13833

Title: Block companion Singer cycles, primitive recursive vector sequences, and coprime polynomial pairs over finite fields
Authors: GHORPADE, SR
RAM, S
Keywords: FEEDBACK SHIFT REGISTERS
FACTORIZATION
Issue Date: 2011
Publisher: ACADEMIC PRESS INC ELSEVIER SCIENCE
Citation: FINITE FIELDS AND THEIR APPLICATIONS,17(5)461-472
Abstract: 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.
URI: http://dx.doi.org/10.1016/j.ffa.2011.02.008
http://dspace.library.iitb.ac.in/jspui/handle/100/13833
ISSN: 1071-5797
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