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|Title:||Primitive polynomials, singer cycles and word-oriented linear feedback shift registers|
UL HASAN, S
|Citation:||DESIGNS CODES AND CRYPTOGRAPHY,58(2)123-134|
|Abstract:||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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