On permutation polynomials over finite fields
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1987-01-01
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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.
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R. A. Mollin and C. Small, “On permutation polynomials over finite fields,” International Journal of Mathematics and Mathematical Sciences, vol. 10, no. 3, pp. 535-543, 1987. doi:10.1155/S0161171287000644