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940,165
Tests and Constructions of Irreducible Polynomials over Finite Fields
 In Foundations of Computational Mathematics
, 1997
"... In this paper we focus on tests and constructions of irreducible polynomials over finite fields. We revisit Rabin's [1980] algorithm providing a variant of it that improves Rabin's cost estimate by a log n factor. We give a precise analysis of the probability that a random polynomial of de ..."
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Cited by 12 (4 self)
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In this paper we focus on tests and constructions of irreducible polynomials over finite fields. We revisit Rabin's [1980] algorithm providing a variant of it that improves Rabin's cost estimate by a log n factor. We give a precise analysis of the probability that a random polynomial
Fast Construction of Irreducible Polynomials over Finite Fields
 J. Symbolic Comput
, 1993
"... The main result of this paper is a new algorithm for constructing an irreducible polynomial of specified degree n over a finite field F q . The algorithm is probabilistic, and is asymptotically faster than previously known algorithms for this problem. It uses an expected number of O~(n 2 + n log q) ..."
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Cited by 64 (6 self)
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The main result of this paper is a new algorithm for constructing an irreducible polynomial of specified degree n over a finite field F q . The algorithm is probabilistic, and is asymptotically faster than previously known algorithms for this problem. It uses an expected number of O~(n 2 + n log q
Generators and irreducible polynomials over finite fields
 Mathematics of Computation
, 1997
"... Abstract. Weil’s character sum estimate is used to study the problem of constructing generators for the multiplicative group of a finite field. An application to the distribution of irreducible polynomials is given, which confirms an asymptotic version of a conjecture of HansenMullen. 1. ..."
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Cited by 32 (7 self)
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Abstract. Weil’s character sum estimate is used to study the problem of constructing generators for the multiplicative group of a finite field. An application to the distribution of irreducible polynomials is given, which confirms an asymptotic version of a conjecture of HansenMullen. 1.
CONSTRUCTING IRREDUCIBLE POLYNOMIALS OVER FINITE FIELDS
"... Abstract. We describe a new method for constructing irreducible polynomials modulo a prime number p. The method mainly relies on Chebotarev’s density theorem. ..."
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Abstract. We describe a new method for constructing irreducible polynomials modulo a prime number p. The method mainly relies on Chebotarev’s density theorem.
New Algorithms for Finding Irreducible Polynomials over Finite Fields
 Mathematics of Computation
, 1990
"... . We present a new algorithm for finding an irreducible polynomial of specified degree over a finite field. Our algorithm is deterministic, and it runs in polynomial time for fields of small characteristic. We in fact prove the stronger result that the problem of finding irreducible polynomials of s ..."
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Cited by 84 (5 self)
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. We present a new algorithm for finding an irreducible polynomial of specified degree over a finite field. Our algorithm is deterministic, and it runs in polynomial time for fields of small characteristic. We in fact prove the stronger result that the problem of finding irreducible polynomials
COUNTING IRREDUCIBLE POLYNOMIALS OVER FINITE FIELDS USING THE INCLUSIONEXCLUSION PRINCIPLE
"... iv ..."
Iterated constructions of irreducible polynomials over finite fields with linearly independent roots
, 2004
"... The paper is devoted to constructive theory of synthesis of irreducible polynomials and irreducible Npolynomials (with linearly independent roots) over finite fields. For a suitably chosen initial Npolynomial F1ðxÞAF2s x of degree n; polynomials FkðxÞAF2s x of degrees 2k1n are constructed by ite ..."
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Cited by 4 (0 self)
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The paper is devoted to constructive theory of synthesis of irreducible polynomials and irreducible Npolynomials (with linearly independent roots) over finite fields. For a suitably chosen initial Npolynomial F1ðxÞAF2s x of degree n; polynomials FkðxÞAF2s x of degrees 2k1n are constructed
Results 1  10
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940,165