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2011
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Primitive polynomials, singer cycles and word-oriented linear feedback shift registers

8 years 6 months ago
Primitive polynomials, singer cycles and word-oriented linear feedback shift registers
Using the structure of Singer cycles in general linear groups, we prove that a conjecture of Zeng, Han and He (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 σ-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 (1995) on the enumeration of splitting subspaces of a given dimension.
Sudhir R. Ghorpade, Sartaj Ul Hasan, Meena Kumari
Added 14 May 2011
Updated 14 May 2011
Type Journal
Year 2011
Where DCC
Authors Sudhir R. Ghorpade, Sartaj Ul Hasan, Meena Kumari
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