Kloosterman sums and primitive elements in Galois fields

Stephen Cohen

Acta Arithmetica (2000)

  • Volume: 94, Issue: 2, page 173-201
  • ISSN: 0065-1036

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Cohen, Stephen. "Kloosterman sums and primitive elements in Galois fields." Acta Arithmetica 94.2 (2000): 173-201. <http://eudml.org/doc/207430>.

@article{Cohen2000,
author = {Cohen, Stephen},
journal = {Acta Arithmetica},
keywords = {Galois fields; trace function; primitive element; character sums; Gauss sums; generalized Kloosterman sums},
language = {eng},
number = {2},
pages = {173-201},
title = {Kloosterman sums and primitive elements in Galois fields},
url = {http://eudml.org/doc/207430},
volume = {94},
year = {2000},
}

TY - JOUR
AU - Cohen, Stephen
TI - Kloosterman sums and primitive elements in Galois fields
JO - Acta Arithmetica
PY - 2000
VL - 94
IS - 2
SP - 173
EP - 201
LA - eng
KW - Galois fields; trace function; primitive element; character sums; Gauss sums; generalized Kloosterman sums
UR - http://eudml.org/doc/207430
ER -

References

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  1. [ChCo] W.-S. Chou and S. D. Cohen, Primitive elements with zero traces, Finite Fields Appl., to appear. 
  2. [Co1] S. D. Cohen, Primitive elements with arbitrary trace, Discrete Math. 83 (1990), 1-7. 
  3. [Co2] S. D. Cohen, Gauss sums and a sieve for generators of Galois fields, Publ. Math. Debrecen 56 (2000) (Kálmán Győry 60th birthday issue), to appear. 
  4. [CoHa1] S. D. Cohen and D. Hachenberger, Primitive normal bases with prescribed trace, Appl. Algebra Engrg. Comm. Comput. 9 (1999), 383-403. Zbl0931.12002
  5. [CoHa2] S. D. Cohen and D. Hachenberger, Primitivity, freeness, norm and trace, Discrete Math. 214 (2000), 135-144. 
  6. [Ha] W. B. Han, The coefficients of primitive polynomials over finite fields, Math. Comp. 65 (1996), 331-340. Zbl0865.11081
  7. [HaMu] T. Hansen and G. L. Mullen, Primitive polynomials over finite fields, ibid. 59 (1992), 639-643. Zbl0770.11053
  8. [Ju] D. Jungnickel, Finite Fields. Structures and Arithmetics, Bibliographisches Institut, Mannheim, 1993. 
  9. [JuVu] D. Jungnickel and S. A. Vanstone, On primitive polynomials over finite fields, J. Algebra 124 (1989), 337-353. Zbl0694.12013
  10. [LiNi] R. Lidl and H. Niederreiter, Finite Fields, Addison-Wesley, Reading, MA, 1983; 2nd ed., Cambridge Univ. Press, Cambridge, 1997. Zbl0554.12010
  11. [MoMu] I. H. Morgan and G. L. Mullen, Primitive normal polynomials over finite fields, Math. Comp. 63 (1994), 759-765. Zbl0805.11083
  12. [Mu] G. L. Mullen, Bases and the distribution of irreducible and primitive polynomials over finite fields, in: Applications of Finite Fields, Inst. Math. Appl. Conf. Ser. New Ser. 59, 1996, 1-18. Zbl0877.11068
  13. [Ni] H. Niederreiter, An enumeration formula for certain irreducible polynomials with an application to the construction of irreducible polynomials over the binary fields, Appl. Algebra Engrg. Comm. Comput. 1 (1990), 119-124. Zbl0726.11077

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