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Complete mappings of finite fields

Published online by Cambridge University Press:  09 April 2009

Harald Niederreiter  and
Karl H. Robinson
Harald Niederreiter
Affiliation:
Kommission für Mathematik Österreichische Akademie der Wissenschaften Dr. Ignaz-Seipel-Platz 2 A-1010 WienAustria
Karl H. Robinson
Affiliation:
Department of Mathematics University of the West IndiesKingston 7Jamaica
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Abstract

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We discuss complete mapping polynomials of finite fields, which are a special class of permutation polynomials. Complete mapping polynomials of small degree are classified. Results are obtained on a class of complete mapping binomials and on permutation binomials.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 33 , Issue 2 , October 1982 , pp. 197 - 212
Copyright
Copyright © Australian Mathematical Society 1982

References

1.Carlitz, L., ‘Some theorems on permutation polynomials,’ Bull. Amer. Math. Soc. 68 (1962), 120–122.CrossRefGoogle Scholar
2.Carlitz, L., ‘Permutations in finite fields,’ Acta Sci. Math.(Szeged) 24 (1963), 196–203.Google Scholar
3.Dénes, J. and Keedwell, A. D., Latin squares and their applications (Academic Press, New York, 1974).Google Scholar
4.Dickson, L. E., ‘The analytic representation of substitutions on a power of a prime number of letters with a discussion of the linear group,’ Ann. of Math. (1) 11 (1896/1897), 65–120.CrossRefGoogle Scholar
5.Dickson, L. E., Linear groups (Dover, New York, 1958).Google Scholar
6.Hall, M. Jr, Combinatorial theory (Blaisdell Publ. Co., Waltham, Mass., 1967).Google Scholar
7.Lausch, H. and Nöbauer, W., Algebra of polynomials (North-Holland, Amsterdam, 1973).Google Scholar
8.Mann, H. B., ‘The construction of orthogonal latin squares,’ Ann. Math. Statist. 13 (1942), 418–423.CrossRefGoogle Scholar
9.Niederreiter, H. and Robinson, K. H., ‘Bol loops of order pq,’ Math. Proc. Cambridge Philos. Soc. 89 (1981), 241–256.CrossRefGoogle Scholar
10.Schmidt, W. M., ‘Zur Methode von Stepanov,’ Acta Arith. 24 (1973), 347–367.CrossRefGoogle Scholar
11.Schmidt, W. M., Equations over finite fields (Lecture Notes in Math., Vol. 536, Springer-Verlag, Berlin-Heidelberg-New York, 1976).Google Scholar