Block companion Singer cycles, primitive recursive vector sequences, and coprime polynomial pairs over finite fields
DSpace at IIT Bombay
View Archive InfoField | Value | |
Title |
Block companion Singer cycles, primitive recursive vector sequences, and coprime polynomial pairs over finite fields
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Creator |
GHORPADE, SR
RAM, S |
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Subject |
FEEDBACK SHIFT REGISTERS
FACTORIZATION Singer cycle Block companion matrix Multiple recursive matrix method Linear feedback shift register (LFSR) Splitting subspace Toeplitz matrix |
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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.
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Publisher |
ACADEMIC PRESS INC ELSEVIER SCIENCE
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Date |
2012-06-26T06:44:24Z
2012-06-26T06:44:24Z 2011 |
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Type |
Article
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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 |
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Language |
English
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