Number Theory

Finite Fields

11Txx

  1. R. D. Baker, G. L. Ebert, K. H. Leung, and Q. Xiang, A trace conjecture and flag-transitive affine planes, J. Combin. Theory Ser. A 95 (2001), no. 1, 158–168.[MR]
  2. Aart Blokhuis, Robert S. Coulter, Marie Henderson, and Christine M. O'Keefe, Permutations amongst the Dembowski-Ostrom polynomials, Finite fields and applications (Augsburg, 1999), Springer, Berlin, 2001, pp. 37–42.[MR]
  3. Carl Bracken, Eimear Byrne, Nadya Markin, and Gary McGuire, A few more quadratic APN functions, preprint (2008), 12 pages.[arXiv]
  4. Carl Bracken, Eimear Byrne, Nadya Markin, and Gary McGuire, New families of quadratic almost perfect nonlinear trinomials and multinomials, Finite Fields Appl. 14 (2008), no. 3, 703–714.[MR]
  5. Marcus Brinkmann and Gregor Leander, On the classification of APN functions up to dimension five, Des. Codes Cryptogr. 49 (2008), no. 1-3, 273–288.[MR]
  6. Jessica F. Burkhart, Neil J. Calkin, Shuhong Gao, Justine C. Hyde-Volpe, Kevin James, Hiren Maharaj, Shelly Manber, Jared Ruiz, and Ethan Smith, Finite field elements of high order arising from modular curves, Des. Codes Cryptogr. 51 (2009), no. 3, 301–314.[MR/doi]
  7. Murat Cenk and Ferruh Özbudak, On multiplication in finite fields, J. Complexity 26 (2010), no. 2, 172–186.[doi]
  8. Mihai Cipu, Dickson polynomials that are permutations, Serdica Math. J. 30 (2004), no. 2-3, 177–194.[MR]
  9. Mihai Cipu and Stephen D. Cohen, Dickson polynomial permutations, Finite Fields and Applications, Contemporary Mathematics, vol. 461, 2008, 79–91 pages.
  10. Stephen D. Cohen, Finite field elements with specified order and traces, Des. Codes Cryptogr. 36 (2005), no. 3, 331–340.[MR]
  11. Stephen D. Cohen, Primitive polynomials with a prescribed coefficient, Finite Fields Appl. 12 (2006), no. 3, 425–491.[MR]
  12. Robert S. Coulter, George Havas, and Marie Henderson, Giesbrecht's algorithm, the HFE cryptosystem and Ore's ps-polynomials, Computer Mathematics (Matsuyama, 2001), Lecture Notes Ser. Comput, vol. 9, World Sci. Publ., River Edge, NJ, 2001, pp. 36–45.[MR]
  13. Robert S. Coulter, George Havas, and Marie Henderson, On decomposition of sub-linearised polynomials, J. Aust. Math. Soc. 76 (2004), no. 3, 317–328.[MR/doi]
  14. Robert S. Coulter and Marie Henderson, The compositional inverse of a class of permutation polynomials over a finite field, Bull. Austral. Math. Soc. 65 (2002), no. 3, 521–526.[MR]
  15. Jean-Marc Couveignes and Reynald Lercier, Elliptic periods for finite fields, Finite Fields Appl. 15 (2009), no. 1, 1–22.[MR/doi]
  16. Yves Edel and Alexander Pott, A new almost perfect nonlinear function which is not quadratic, Adv. Math. Commun. 3 (2009), no. 1, 59–81.[MR/doi]
  17. Ronald Evans, Henk D. L. Hollmann, Christian Krattenthaler, and Qing Xiang, Gauss sums, Jacobi sums, and p-ranks of cyclic difference sets, J. Combin. Theory Ser. A 87 (1999), no. 1, 74–119.[MR]
  18. Reza Rezaeian Farashahi and Ruud Pellikaan, The quadratic extension extractor for (hyper)elliptic curves in odd characteristic, Arithmetic of finite fields, Lecture Notes in Comput. Sci., vol. 4547, Springer, Berlin, 2007, pp. 219–236.[MR]
  19. Kseniya Garaschuk, On binary and ternary Kloosterman sums, PhD Thesis, Simon Fraser University, 2007.
  20. Lenwood S. Heath and Nicholas A. Loehr, New algorithms for generating Conway polynomials over finite fields, in Proceedings of the Tenth Annual ACM-SIAM Symposium on Discrete Algorithms (Baltimore, MD, 1999), ACM, New York, 1999, pp. 429–437.[MR]
  21. Dae San Kim, Codes associated with O+(2n,2r) and power moments of Kloosterman sums, preprint (2008), 9 pages.[arXiv]
  22. Dae San Kim, Codes associated with orthogonal groups and power moments of Kloosterman sums, preprint (2008).[arXiv]
  23. Dae San Kim, Codes associated with special linear groups and power moments of multi-dimensional Kloosterman sums, preprint (2008), 7 pages.[arXiv]
  24. Douglas A. Leonard, A weighted module view of integral closures of affine domains of type I, Adv. Math. Commun. 3 (2009), no. 1, 1-11.
  25. Petr Lisoněk, On the connection between Kloosterman sums and elliptic curves, Sequences and Their Applications – SETA 2008: Proceedings, Lecture Notes in Computer Science, vol. 5203, Springer, Berlin Heidelberg, 2008, pp. 182–187.
  26. Marko Moisio, Kloosterman sums, elliptic curves, and irreducible polynomials with prescribed trace and norm, Acta Arith. 132 (2008), no. 4, 329–350.[MR/arXiv]
  27. Ferruh Özbudak, Elements of prescribed order, prescribed traces and systems of rational functions over finite fields, Des. Codes Cryptogr. 34 (2005), no. 1, 35–54.[MR]
  28. B. V. Petrenko, On the product of two primitive elements of maximal subfields of a finite field, J. Pure Appl. Algebra 178 (2003), no. 3, 297–306.[MR]
  29. B. V. Petrenko, On the sum of two primitive elements of maximal subfields of a finite field, Finite Fields Appl. 9 (2003), no. 1, 102–116.[MR]
  30. Håvard Raddum and Igor Semaev, Solving multiple right hand sides linear equations, Des. Codes Cryptogr. 49 (2008), no. 1-3, 147–160.[MR/eprint]