N. Zierler and J. Brillhart, "On primitive trinomials (mod 2)", Information and Control 13 (1968), 541-554. Home/Search Document Not in Database Summary Related Articles Check |
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On the Periods of Generalized Fibonacci Recurrences - Brent (1992) (6 citations) (Correct)
....(mod 2) if = 2 r Gamma 1. Note that primitivity is a stronger condition than irreducibility 1 , i.e. Q(t) primitive implies that Q(t) is irreducible, but the converse is not generally true unless 2 r Gamma 1 is prime 2 . Tables of irreducible and primitive trinomials are available [4, 10, 14, 16, 20, 22, 23, 24, 25]. In the following we usually assume that Q(t) is irreducible. Our assumption that q 0 and q r are odd excludes the trivial case Q(t) t, and implies that Q(t) is irreducible (or primitive) of degree r iff the same is true of Q(t) We are interested in the period pw of the sequence (x n ) ....
N. Zierler and J. Brillhart, "On primitive trinomials (mod 2)", Information and Control, 13 (1968), 541-554. MR 38#5750.
Uniform Random Number Generators for Vector and Parallel Computers - Brent (1992) (3 citations) (Correct)
....most r Gamma 1 determined by the initial values U 0 ; U r Gamma1 . For example, if m = 2 and the initial values are not all zero, then the sequence has maximal period 2 r Gamma 1 if and only if Q(x) is a primitive polynomial (mod 2) Tables of such primitive polynomials are available [36, 37]. Verification is particularly simple if r is the exponent of a Mersenne prime (i.e. 2 r Gamma 1 is prime) because then we only need to check that x = x 2 r mod (Q(x) 2) which can be done by r squarings of polynomials (mod 2) involving a total of only O(r 2 ) operations [38] The more ....
N. Zierler and J. Brillhart, "On primitive trinomials (mod 2)", Information and Control 13 (1968), 541-554.
Uniform Random Number Generators for Vector and Parallel Computers - Brent (1992) (3 citations) (Correct)
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N. Zierler and J. Brillhart, "On primitive trinomials (mod 2)", Information and Control 13 (1968), 541-554.
Uniform Random Number Generators for Supercomputers - Brent (1992) (10 citations) (Correct)
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N. Zierler and J. Brillhart, "On primitive trinomials (mod 2)", Information and Control 13 (1968), 541-554. Part II, ibid 14 (1969), 566-569.
Uniform Random Number Generators for Supercomputers - Brent (1992) (10 citations) (Correct)
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N. Zierler and J. Brillhart, "On primitive trinomials (mod 2)", Information and Control 13 (1968), 541-554. Part II, ibid 14 (1969), 566-569.
Handbook of Applied Cryptography - References - Menezes, van Oorschot, Vanstone (Correct)
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N. ZIERLER AND J. BRILLHART, "On primitive trinomials (mod 2)", Information and Control, 13 (1968), 541--554.
This is a Chapter from the Handbook of Applied Cryptography - Menezes, van Oorschot.. (1996) (Correct)
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N. ZIERLER AND J. BRILLHART, "On primitive trinomials (mod 2)", Information and Control, 13 (1968), 541--554.
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