On the Periods of Generalized Fibonacci Recurrences1
نویسنده
چکیده
We give a simple condition for a linear recurrence (mod 2w) of degree r to have themaximal possible period 2w 1(2r 1). It follows that the period is maximal in the casesof interest for pseudo-random number generation, i.e. for 3-term linear recurrences de nedby trinomials which are primitive (mod 2) and of degree r > 2. We consider the enumera-tion of certain exceptional polynomials which do not give maximal period, and list all suchpolynomials of degree less than 15.
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