Primitive polynomials, singer cycles and word-oriented linear feedback shift registers
DSpace at IIT Bombay
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Title |
Primitive polynomials, singer cycles and word-oriented linear feedback shift registers
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Creator |
GHORPADE, SR
UL HASAN, S KUMARI, M |
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Subject |
Primitive polynomial
Linear Feedback Shift Register (LFSR) Primitive recursive vector sequence Singer cycle Singer subgroup Splitting subspaces |
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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.
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Publisher |
SPRINGER
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Date |
2012-06-26T05:24:24Z
2012-06-26T05:24:24Z 2011 |
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Type |
Article
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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 |
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Language |
English
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