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Abstract: We discuss a number of open problems and conjectures in the theory and application of finite fields. We also provide a brief discussion of the status as well as references related to each problem. 1 Introduction In this paper we try to summarise some interesting and/or important questions in the theory and application of finite fields. These questions obviously reflect our personal tastes but we have indeed tried to consider questions of general interest. We hope that these questions and even... (Update)
Context of citations to this paper: More
...5.33, 5.22, and 6.47, respectively. This is indeed verified by our computation. These polynomials provide examples for Problem 27 in [28]. We also did an experiment on the existence of irreducible polynomials of the form x g(x) # F q [x] with deg g(x) log n O(1) For q = 2...
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BibTeX entry: (Update)
G.L. Mullen and I.E. Shparlinski, Open problems and conjectures in finite fields. In Finite Fields and Applications (S.D. Cohen and H. Niederreiter Eds.), Cambridge University Press, Lecture Note Series of London Math. Society, Vol. 233 (1996), 243-268. http://citeseer.ist.psu.edu/mullen96open.html More
@misc{ mullen96open,
author = "G. Mullen and I. Shparlinski",
title = "Open problems and conjectures in finite fields",
text = "G.L. Mullen and I.E. Shparlinski, Open problems and conjectures in finite
fields. In Finite Fields and Applications (S.D. Cohen and H. Niederreiter
Eds.), Cambridge University Press, Lecture Note Series of London Math. Society,
Vol. 233 (1996), 243-268.",
year = "1996",
url = "citeseer.ist.psu.edu/mullen96open.html" }
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16 Optimal normal bases - Gao, Lenstra - 1992
12 When does a polynomial over a finite field permute the eleme.. (context) - Lidl, Mullen - 1988
12 When does a polynomial over a finite field permute the eleme.. (context) - Lidl, Mullen - 1993
11 Digital nets and sequences constructed over finite rings and.. (context) - Larcher, Niederreiter et al.
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10 Low complexity normal bases (context) - Ash, Blake et al. - 1989
7 On orders of optimal normal basis generators - Gao, Vanstone - 1995
7 Point sets with uniformity properties and orthogonal hypercu.. (context) - Mullen, Whittle - 1992
6 On Artin's conjecture and Euclid's algorithm in global field.. (context) - Lenstra - 1977
6 Permutation polynomials over finite fields (context) - Mullen - 1993
6 Primitive polynomials over finite fields (context) - Hansen, Mullen - 1992
5 Primitive normal bases for finite fields (context) - Lenstra, Schoof - 1987
4 the distribution of residues of finitely generated multiplic.. (context) - Konyagin, Shparlinski - 1995
4 Combinatorial Bounds and Constructions in the Theory of Unif.. (context) - Lawrence - 1995
4 Self-complementary normal bases in finite fields (context) - Lempel, Weinberger - 1988
3 A characterization of the extremal distribution of optimal n.. (context) - Mullin - 1993
3 Eine Verscharfung des Satzes von der Normalbasis (context) - Blessenohl, Johnsen - 1986
3 Primitive elements and polynomials with arbitrary trace (context) - Cohen - 1990
3 Orders of Gauss periods in finite fields (context) - Gathen, Shparlinski
2 Tests for permutation functions (context) - Ma, Gathen - 1995
2 Primitive normal polynomials over finite fields (context) - Morgan, Mullen - 1994
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2 Primitive elements and polynomials: Existence results (context) - Cohen - 1993
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1 Factoring polynomials in finite fields: An application of La.. (context) - Katz - 1990
1 Polynomial factorization and the construction of regular dir.. (context) - Cohen - 1995
1 On estimates of Gaussian sums and Waring (context) - Konyagin - 1992
1 Vanstone and R (context) - Mullin, Onyszchuk
1 Tables of (t; m; s)- net and (t; s)-sequence parameters (context) - Mullen, Mahalanabis et al. - 1995
1 Completely normal primitive basis generators of finite field.. (context) - Morgan, Mullen
1 Bases and the distribution of irreducible and primitive poly.. (context) - Mullen - 1994
1 Primitive polynomials of low weight (context) - Hansen, Mullen - 1993
1 Distribution of primitive normal polynomials (context) - Morgan, Mullen - 1994
1 Now distributed by Camb (context) - Lidl, Niederreiter et al. - 1983
1 Normal bases and completely free elements in prime power ext.. (context) - Hachenberger - 1996
1 Almost weakly self-dual bases for finite fields (context) - Morgan, Mullen et al.
1 Permutation polynomials: A matrix analogue of Schur (context) - Mullen - 1995
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