Hostname: page-component-848d4c4894-xm8r8 Total loading time: 0 Render date: 2024-06-19T23:04:25.486Z Has data issue: false hasContentIssue false

The compositional inverse of a class of permutation polynomials over a finite field

Published online by Cambridge University Press:  17 April 2009

Robert S. Coulter
Affiliation:
School of Computing and Mathematics, Deakin University, 221 Burwood Highway, Burwood Vic 3123, Australia, e-mail: shrub@deakin.edu.au
Marie Henderson
Affiliation:
Centre for Discrete Mathematics and Computing Department of Computer Science and Electrical Engineering, The University of Queensland, Queensland 4072, Australia, e-mail: marie@itee.uq.edu.au
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.

A new class of bilinear permutation polynomials was recently identified. In this note we determine the class of permutation polynomials which represents the functional inverse of the bilinear class.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Blokhuis, A., Coulter, R.S., Henderson, M. and O'Keefe, C.M., ‘Permutations amongst the Dembowski-Ostrom polynomials’,in Finite Fields and Applications: Proceedings of the Fifth International Conference on Finite Fields and Applications, (Jungnickel, D. and Niederreiter, H., Editors) (Springer-Verlag, Berlin, 2001), pp. 3742.Google Scholar
[2]Bosma, W., Cannon, J. and Playoust, C., ‘The Magma algebra system I: The user language’, J. Symbolic Comput. 24 (1997), 235265.CrossRefGoogle Scholar
[3]Lidl, R. and Mullen, G.L., ‘When does a polynomial over a finite field permute the elements of the field?’, Amer. Math. Monthly 95 (1988), 243246.CrossRefGoogle Scholar
[4]Lidl, R. and Mullen, G.L., ‘When does a polynomial over a finite field permute the elements of the field?, II’, Amer. Math. Monthly 100 (1993), 7174.CrossRefGoogle Scholar
[5]Lidl, R., Mullen, G.L. and Turnwald, G., Dickson Polynomials, Pitman Monographs and Surveys in Pure and Appl. Math. 65 (Longman Scientific and Technical, Essex, England, 1993).Google Scholar
[6]Mullen, G.L., ‘Permutation polynomials: a matrix analogue of schur's conjecture and a survey of recent results’, Finite Fields Appl. 1 (1995), 242258.CrossRefGoogle Scholar