On the Periods of Generalized Fibonacci Recurrences (1992)
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Richard P. Brent
| Citations: | 28 - 10 self |
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@MISC{Brent92onthe,
author = {Richard P. Brent},
title = {On the Periods of Generalized Fibonacci Recurrences},
year = {1992}
}
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Abstract
We give a simple condition for a linear recurrence (mod 2 w ) of degree r to have the maximal possible period 2 w 1 (2 r 1). It follows that the period is maximal in the cases of interest for pseudo-random number generation, i.e. for 3-term linear recurrences dened by trinomials which are primitive (mod 2) and of degree r > 2. We consider the enumeration of certain exceptional polynomials which do not give maximal period, and list all such polynomials of degree less than 15. 1.
