Name
Title | ||
|---|---|---|
Primitive polynomials, singer cycles and word-oriented linear feedback shift registers |
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: 驴-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 驴-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. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1007/s10623-010-9387-7 | Des. Codes Cryptography |
Keywords | DocType | Volume |
Primitive polynomial,Linear Feedback Shift Register (LFSR),Primitive recursive vector sequence,Singer cycle,Singer subgroup,Splitting subspaces,11T06,11T71,20G40,94A60 | Journal | 58 |
Issue | ISSN | Citations |
2 | Designs, Codes and Cryptography, Vol. 58, No. 2 (2011), pp.
123-134 | 15 |
PageRank | References | Authors |
1.11 | 3 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Sudhir R. Ghorpade | 1 | 80 | 12.16 |
| Sartaj Ul Hasan | 2 | 37 | 4.25 |
| M. V. P. Kumar | 3 | 21 | 3.98 |