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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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On the periods of generalized Fibonacci recurrences
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by Richard P. Brent PDF
Math. Comp. 63 (1994), 389-401 Request permission

Abstract:

We give a simple condition for a linear recurrence $\pmod {2^w}$ 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 pseudorandom number generation, i.e., for three-term linear recurrences defined by trinomials which are primitive $\pmod 2$ 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.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Math. Comp. 63 (1994), 389-401
  • MSC: Primary 11B37; Secondary 11B39
  • DOI: https://doi.org/10.1090/S0025-5718-1994-1216256-7
  • MathSciNet review: 1216256