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A NOTE ON INTERPOLATION OF PERMUTATIONS OF A SUBSET OF A FINITE FIELD

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

Published online by Cambridge University Press:  15 May 2014

CHRIS CASTILLO ,
ROBERT S. COULTER  and
STEPHEN SMITH
CHRIS CASTILLO
Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA
ROBERT S. COULTER*
Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA email coulter@math.udel.edu
STEPHEN SMITH
Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA
*
✉coulter@math.udel.edu
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Abstract

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We determine several variants of the classical interpolation formula for finite fields which produce polynomials that induce a desirable mapping on the nonspecified elements, and without increasing the number of terms in the formula. As a corollary, we classify those permutation polynomials over a finite field which are their own compositional inverse, extending work of C. Wells.

Keywords

interpolationpermutation polynomials

MSC classification

Secondary: 11T06: Polynomials 12E10: Special polynomials
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 90 , Issue 2 , October 2014 , pp. 213 - 219
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

References

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