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Articles

Rational functions of degree four that permute the projective line over a finite field

Pages 3798-3809 | Received 08 Nov 2020, Accepted 27 Feb 2021, Published online: 15 Apr 2021

References

  • Dickson, L. E. (1896). The analytic representation of substitutions on a power of a prime number of letters with a discussion of the linear group. Ann. Math. 11(1/6):65–120. DOI: 10.2307/1967217.
  • Fan, X. (2018). A classification of permutation polynomials of degree 7 over finite fields, arXiv:1812.02080.
  • Fan, X. (2019). Permutation polynomials of degree 8 over finite fields of characteristic 2, arXiv:1903.10309.
  • Ferraguti, A., Micheli, G. (2020). Full classification of permutation rational functions and complete rational functions of degree three over finite fields. Des. Codes Cryptogr. 88(5):867–886. DOI: 10.1007/s10623-020-00715-0.
  • Fulton, W. (1989). Algebraic Curves. New York: Addison-Wesley Publishing Co.
  • Hicks, K., Hou, X., Mullen, G. L. (2012). Sums of reciprocals of polynomials over finite fields. Amer. Math. Monthly 119:313–317.
  • Hou, X. (2020). A power sum formula by Carlitz and its applications to permutation rational functions of finite fields, arXiv:2003.02246.
  • Li, J., Chandler, D. B., Xiang, Q. (2010). Permutation polynomials of degree 6 or 7 over finite fields of characteristic 2. Finite Fields Appl. 16(6):406–419. DOI: 10.1016/j.ffa.2010.07.001.
  • Shallue, C. J., Wanless, I. M. (2013). Permutation polynomials and orthomorphism polynomials of degree six. Finite Fields Appl. 20:94–92.
  • Stichtenoth, H. (2009). Algebraic Function Fields and Codes, 2nd ed. Berlin: Springer.

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