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Primitive polynomials, singer cycles and word-oriented linear feedback shift registers

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Title Primitive polynomials, singer cycles and word-oriented linear feedback shift registers
 
Creator GHORPADE, SR
UL HASAN, S
KUMARI, M
 
Subject Primitive polynomial
Linear Feedback Shift Register (LFSR)
Primitive recursive vector sequence
Singer cycle
Singer subgroup
Splitting subspaces
 
Description Using the structure of Singer cycles in general linear groups, we prove that a conjecture of Zeng et al. (Word-Oriented Feedback Shift Register: sigma-LFSR, 2007) holds in the affirmative in a special case, and outline a plausible approach to prove it in the general case. This conjecture is about the number of primitive sigma-LFSRs of a given order over a finite field, and it generalizes a known formula for the number of primitive LFSRs, which, in turn, is the number of primitive polynomials of a given degree over a finite field. Moreover, this conjecture is intimately related to an open question of Niederreiter (Finite Fields Appl 1:3-30, 1995) on the enumeration of splitting subspaces of a given dimension.
 
Publisher SPRINGER
 
Date 2012-06-26T05:24:24Z
2012-06-26T05:24:24Z
2011
 
Type Article
 
Identifier DESIGNS CODES AND CRYPTOGRAPHY,58(2)123-134
0925-1022
http://dx.doi.org/10.1007/s10623-010-9387-7
http://dspace.library.iitb.ac.in/jspui/handle/100/13961
 
Language English