Hostname: page-component-cc8bf7c57-n7pht Total loading time: 0 Render date: 2024-12-11T23:00:22.906Z Has data issue: false hasContentIssue false

A note on the permutation behaviour of the Dickson polynomials of the second kind

Published online by Cambridge University Press:  17 April 2009

M. Henderson
Affiliation:
School of Information TechnologyThe University of QueenslandQueensland 4072Australia e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this note known factorisation results for the Dickson polynomials of the second kind, fk(X, a), are used to obtain simple restrictions on those k for which fk(X, a) is a permutation polynomial over Fq.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Chou, W.S., ‘The factorization of Dickson polynomials over finite fields’, Finite Fields Appl. 3 (1997), 8496.CrossRefGoogle Scholar
[2]Cohen, S.D., ‘Dickson polynomials of the second kind that are permutations’, Canad. J. Math 46 (1994), 225238.CrossRefGoogle Scholar
[3]Cohen, S.D., ‘Dickson permutations’, in Number-theoretic and algebraic methods in Computer Science (Moscow 1993) (World Scientific Publishing, River Edge, NJ. 1995), pp. 2951.Google Scholar
[4]Henderson, M. and Matthews, R., ‘Permutation properties of Chebyshev polynomials of the second kind over a finite field’, Finite Fields Appl. 1 (1995), 115125.CrossRefGoogle Scholar
[5]Lidl, R., Mullen, G.L. and Turnwald, G., Dickson polynomials, Pitman Monographs and Surveys in Pure and Applied Maths 65 (Longman Scientific and Technical, Essex, England, 1993).Google Scholar
[6]Lidl, R. and Niederreiter, H., Finite fields, Encyclopedia Math. Appl. 20 (Addison-Wesley, Reading, 1983), (now distributed by Cambridge University Press).Google Scholar
[7]Matthews, R., Permutation polynomials in one and several variables, Ph.D. Thesis (University of Tasmania, Tasmania, Australia, 1982).Google Scholar