Elsevier

Discrete Mathematics

Volume 80, Issue 1, 15 February 1990, Pages 97-100
Discrete Mathematics

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A note on permutation polynomials and finite geometries

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Abstract

A polynomial ƒ over a finite field F is called a difference permutation polynomial if the mapping x → ƒ(x + a) − ƒ(x) is a permutation of F for each nonzero element a of F. Difference permutation polynomials give rise to affine planes. We show that when F = GF(p), where p is a prime, the only difference permutation polynomials over F are quadratic.

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Research partially supported by the National Security Agency and the Deutsche Forschungsgemeinschaft.