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Am-permutation polynomials

Part of: Finite fields and commutative rings (number-theoretic aspects)

Published online by Cambridge University Press:  09 April 2009

Sangtae Jeong
Sangtae Jeong
Affiliation:
Department of Mathematics, Inha University, Incheon 402–751, Korea, e-mail: stj@math.inha.ac.kr
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Abstract

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We introduce a class of polynomials which induce a permutation on the set of polynomials in one variable of degree less than m over a finite field. We call then Am-permutation polynomials. We also give three criteria to characterize such polynomials.

Keywords

Am-permutation polynomials(extended) Hermite-Dickson criterionCarlitz polynomials.

MSC classification

Secondary: 11T06: Polynomials 11T55: Arithmetic theory of polynomial rings over finite fields
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 80 , Issue 2 , April 2006 , pp. 149 - 158
Copyright
Copyright © Australian Mathematical Society 2006

References

[1]Carlitz, L., ‘A set of polynomials’, Duke Math. J. 6 (1940), 486–504.Google Scholar
[2]Carlitz, L. and Lutz, J. A., ‘A characterizaton of permuation polynomials over a finite field’, Amer. Math. Mon. 85 (1978), 746–748.CrossRefGoogle Scholar
[3]Dickson, L. E., ‘The analytic representation of substitutions on a power of a prime number of letters with a discussion of the linear group’, Ann. of Math. 11 (1897), 65–120, 161–183.CrossRefGoogle Scholar
[4]Goss, D., Basic structures of function field arithmetic (Springer, Berlin, 1996).CrossRefGoogle Scholar
[5]Hermite, C., ‘Sur les fonctions de sept lettres’, C.R. Acad. Sci. Paris 57 (1863), 750–757; Oeuvres, 2, 280–288, (Gauthier-Villars, Paris, 1908).Google Scholar
[6]Levine, J. and Brawley, J. V., ‘Some cryptographic applications of permutation polynomials’, Cryptologia 1 (1977), 76–92.CrossRefGoogle Scholar
[7]Lidl, R. and Niederreiter, H., ‘On orthogonal systems and permutation polynomials in several variables’, Acta Arith. 22 (1972), 257–265.Google Scholar
[8]Lidl, R. and Niederreiter, H., Finite fields, Encyclopedia Math. Appl. 20 (Addison-Wesley, Reading, MA, 1983).Google Scholar
[9]Schmidt, W. M., Equations over finite fields—an elementary approach, Lecture Notes in Math. 536 (Springer, Berlin, 1976).CrossRefGoogle Scholar