Dickson Polynomials Over Finite Fields and Complete Mappings
1987 ◽
Vol 30
(1)
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pp. 19-27
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Keyword(s):
AbstractDickson polynomials over finite fields are familiar examples of permutation polynomials, i.e. of polynomials for which the corresponding polynomial mapping is a permutation of the finite field. We prove that a Dickson polynomial can be a complete mapping polynomial only in some special cases. Complete mapping polynomials are of interest in combinatorics and are defined as polynomials f(x) over a finite field for which both f(x) and f(x) + x are permutation polynomials. Our result also verifies a special case of a conjecture of Chowla and Zassenhaus on permutation polynomials.
1990 ◽
Vol 49
(2)
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pp. 309-318
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2008 ◽
Vol 04
(05)
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pp. 851-857
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1982 ◽
Vol 33
(2)
◽
pp. 197-212
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Keyword(s):
2005 ◽
Vol 2005
(16)
◽
pp. 2631-2640
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1987 ◽
Vol 10
(3)
◽
pp. 535-543
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2016 ◽
Vol 15
(07)
◽
pp. 1650133
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Several classes of permutation trinomials from Niho exponents over finite fields of characteristic 3
2019 ◽
Vol 18
(04)
◽
pp. 1950069
1969 ◽
Vol 7
(1)
◽
pp. 49-55
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