Gao, S., and Mullen, G. Dickson polynomials and irreducible polynomials over #nite #elds. J. Number Theory 49 #1994#, 118#132. Home/Search Document Not in Database Summary Related Articles Check |
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Factoring Dickson polynomials over finite fields - Bhargava, Zieve (1997) (Correct)
....of a finite field was known, due to K. S. Williams for n odd [7] and to G. Turnwald for n even [5, Prop. 1.7] we give simpler proofs of these results as well. As another application of our methods, one can give a short and simple proof of the irreducibility criterion for D n (X; a) b from [3], and further one can describe the complete factorization of any such polynomial over any finite field. We shall retain the notation of the first paragraph throughout this note. Also, for any 2 F q , by p we shall mean a fixed square root of in F q ; for any positive integer d coprime to p, ....
S. Gao and G. L. Mullen, Dickson polynomials and irreducible polynomials over finite fields, J. Number Theory 49 (1994), 118--132.
Orders of Gauß Periods in Finite Fields - Gathen, Shparlinski (1998) (1 citation) (Correct)
....q) O(1) probabilistically, # r O(1) q 1 2 log q deterministically, # (r log q) O(1) deterministically under the ERH. More precise forms of these assertions and further details can be found in [21] Section 1.1. In some cases an explicit formula for the minimal polynomial of # is known [7]. If q is a primitive root modulo the prime r, then the minimal polynomial of # is x r 1 . x 1. This can be used in the construction of Theorem 1 below. In this paper we do not estimate the cost of constructing # (which, as we mentioned above, is fairly small) but rather concentrate on ....
S. Gao and G. L. Mullen, `Dickson polynomials and irreducible polynomials over finite fields ' J. Number Theory , 49 (1994), 118--132.
Orders of Gauß Periods in Finite Fields - Gathen, Shparlinski (1998) (1 citation) (Correct)
....O(1) probabilistically, ffi r O(1) q 1=2 log q deterministically, ffi (r log q) O(1) deterministically under the ERH. More precise forms of these assertions and further details can be found in [21] Section 1.1. In some cases an explicit formula for the minimal polynomial of ff is known [7]. If q is a primitive root modulo the prime r, then the minimal polynomial of fi is x r Gamma1 : x 1. This can be used in the construction of Theorem 1 below. In this paper we do not estimate the cost of constructing ff (which, as we mentioned above, is fairly small) but rather ....
S. Gao and G. L. Mullen, `Dickson polynomials and irreducible polynomials over finite fields ' J. Number Theory, 49 (1994), 118--132.
Tests and Constructions of Irreducible Polynomials over Finite.. - Gao, Panario (1997) Self-citation (Gao) (Correct)
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Gao, S., and Mullen, G. Dickson polynomials and irreducible polynomials over #nite #elds. J. Number Theory 49 #1994#, 118#132.
Normal Bases over Finite Fields - Gao (1993) (2 citations) Self-citation (Gao) (Correct)
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S. Gao and G.L. Mullen, "Dickson polynomials and irreducible polynomials over finite fields", 1992, to appear in J. Number Theory.
Constructing Elements Of Large Order In Finite Fields - Gathen, Shparlinski (1999) (Correct)
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S. Gao and G. L. Mullen, `Dickson polynomials and irreducible polynomials over finite fields', J. Number Theory , 49 (1994), 118--132.
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