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Abstract: this paper are new, we do not give complete detailed proofs but indicate the underlying ideas. Here we present a list of possible applications (which is certainly incomplete). We start from pointing out some general purpose applications: ffl Coding Theory : AP1, AP3, AP6 (Update)
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BibTeX entry: (Update)
@misc{ shparlinski-approximate,
author = "Igor Shparlinski",
title = "Approximate Constructions In Finite Fields",
url = "citeseer.ist.psu.edu/134456.html" }
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51 On distinguishing prime numbers from composite numbers (context) - Adleman, Pomerance et al. - 1983
43 Highly resilient correctors for polynomials - Gemmell, Sudan - 1992
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35 New algorithms for finding irreducible polynomials over fini.. - Shoup - 1990
32 On zero testing and interpolation of k-sparse multivariate p.. (context) - Clausen, Dress et al. - 1991
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24 A rigorous time bound for factoring integers (context) - Lenstra, Pomerance - 1992
23 Finding irreducible polynomials over finite fields (context) - Adleman, Lenstra - 1986
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12 Quadratic fields and factorization (context) - Schoof - 1984
12 An estimate for character sums (context) - Katz - 1989
10 On character sums and primitive roots (context) - Burgess - 1962
9 The complexity of sparse polynomials interpolation over fini.. (context) - Werther - 1994
7 Class number, a theory of factorization and genera (context) - Shanks - 1971
7 On finding primitive roots in finite fields (context) - Shparlinski - 1996
7 On some approximation problems concerning sparse polynomials.. (context) - Karpinski, Shparlinski - 1996
7 the least primitive root of a prime (context) - Wang - 1959
6 the maximal distance between integers composed of small prim.. (context) - Tijdeman - 1974
6 Statistical evidence for small generating sets (context) - Bach, Huelsbergen - 1993
6 On primitive elements in finite fields and on elliptic curve.. (context) - Shparlinski - 1990
4 the distribution of primitive roots in finite fields (context) - Perel'muter, Shparlinski - 1990
4 The computational complexity of recognizing permutation func.. (context) - Ma, Gathen - 1995
4 Kluwer Acad (context) - Computational, in et al. - 1992
4 On primes recognizable in deterministic polynomial time (context) - Konyagin, Pomerance - 1993
4 Addison--Wesley (context) - Lidl, Niederreiter et al. - 1983
3 Distribution of primitive roots in a finite field (context) - Carlitz - 1953
3 Irreducible polynomials over finite fields (context) - Gathen - 1986
3 Orders of Gauss periods in finite fields (context) - Gathen, Shparlinski
2 Constructing nonresidues in finite fields and the Extended R.. - Buchmann, Shoup - 1991
2 Test for permutation functions (context) - Ma, Gathen - 1995
2 Finding irreducible and primitive polynomials (context) - Shparlinski - 1993
1 An improvement of Rabin (context) - Calmet, Loos - 1980
1 Gaps between prime numbers (context) - Baker, Harman - 1995
1 The explicit construction of irreducible polynomials over fi.. (context) - Cohen - 1992
1 Open problems in number theoretic complexity, 2 (context) - Adleman, McCurley - 1994
1 Self-testing/correction with applications to numerical probl.. (context) - Blum, Luby et al. - 1993
1 Bounds on sample space size for matrix products verification - Chinn, Sinha - 1993
1 The construction of a finite field in polynomial time (context) - Chistov - 1984
1 Construction of irreducible polynomials over finite fields w.. (context) - Semaev - 1988
1 Arithmetical properties of Bell numbers to a composite modul.. (context) - Lunnon, Pleasants et al. - 1979
1 A probabylistic algorithm for verifying matrix products usin.. (context) - Kimbrel, Sinha - 1993
1 On arithmetic algorithms over finite fields (context) - Cantor - 1989
Documents on the same site (http://www.comp.mq.edu.au/~igor/Publ.html): More
A Lower Bound for Primality - Allender, Saks, Shparlinski (1999) (Correct)
Finding Points on Curves over Finite Fields - Gathen, Shparlinski, Sinclair (1996) (Correct)
A Public Key Cryptosystem Based On Sparse Polynomials - Grant, Lieman, Shparlinski (1998) (Correct)
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