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On permutation polynomials over finite fields

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  • R. A. Mollin
  • C. Small

Abstract

A polynomial f over a finite field F is called a permutation polynomial if the mapping F → F defined by f is one-to-one. In this paper we consider the problem of characterizing permutation polynomials; that is, we seek conditions on the coefficients of a polynomial which are necessary and sufficient for it to represent a permutation. We also give some results bearing on a conjecture of Carlitz which says essentially that for any even integer m , the cardinality of finite fields admitting permutation polynomials of degree m is bounded.

Suggested Citation

  • R. A. Mollin & C. Small, 1987. "On permutation polynomials over finite fields," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 10, pages 1-9, January.
    • Handle: RePEc:hin:jijmms:393016
    DOI: 10.1155/S0161171287000644
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    Cited by:

    1. Somphong Jitman & Aunyarut Bunyawat & Supanut Meesawat & Arithat Thanakulitthirat & Napat Thumwanit, 2016. "Characterization and Enumeration of Good Punctured Polynomials over Finite Fields," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2016, pages 1-7, March.

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