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On permutation polynomials whose difference is linear

Published online by Cambridge University Press:  18 May 2009

W. W. Stothers
W. W. Stothers
Affiliation:
Department of Mathematics, University Gardens, Glasgow G12 8QW
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Let q be a power of a prime p, and let Sqbe the set of permutations of {0, 1,…, q – 1). As Sq is isomorphic to the group of permutations of Fq, the field of q elements, each element of 5, can be regarded as a polynomial over Fq. Various authors (e.g. [1], [2], [3]) have considered functions f(x) such that

f(x) ∈ Sq, and (f(x) + λ×) ∈ Sq

for some λ ∈ Fq when λ = 1, f(x) is a complete mapping polynomial ([3]).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 32 , Issue 2 , May 1990 , pp. 165 - 171
Copyright
Copyright © Glasgow Mathematical Journal Trust 1990

References

REFERENCES

1.Dickson, L. E., Linear Groups (Dover, 1958).Google Scholar
2.Mullen, G. and Niederreiter, H., The structure of a group of permutation polynomials, J. Austral. Math. Soc. Ser. A 38 (1985), 164–170.CrossRefGoogle Scholar
3.Niederreiter, H. and Robinson, K. H., Complete mappings of finite fields, J. Austral. Math. Soc. Ser. A 33 (1982), 197–212.CrossRefGoogle Scholar