On a Conjecture of Carlitz
1987 ◽
Vol 43
(3)
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pp. 375-384
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Keyword(s):
A conjecture of Carlitz on permutation polynomials is as follow: Given an even positive integer n, there is a constant Cn, such that if Fq is a finite field of odd order q with q > Cn, then there are no permutation polynomials of degree n over Fq. The conjecture is a well-known problem in this area. It is easily proved if n is a power of 2. The only other cases in which solutions have been published are n = 6 (Dickson [5]) and n = 10 (Hayes [7]); see Lidl [11], Lausch and Nobauer [9], and Lidl and Niederreiter [10] for remarks on this problem. In this paper, we prove that the Carlitz conjecture is true if n = 12 or n = 14, and give an equivalent version of the conjecture in terms of exceptional polynomials.
Several classes of permutation trinomials from Niho exponents over finite fields of characteristic 3
2019 ◽
Vol 18
(04)
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pp. 1950069
2019 ◽
Vol 101
(1)
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pp. 40-55
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1985 ◽
Vol 38
(2)
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pp. 164-170
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2002 ◽
Vol 8
(4)
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pp. 478-490
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2012 ◽
Vol 55
(2)
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pp. 418-423
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2016 ◽
Vol 12
(06)
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pp. 1519-1528
1977 ◽
Vol 29
(1)
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pp. 169-179
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1968 ◽
Vol 16
(1)
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pp. 1-17
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2018 ◽
Vol 2018
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pp. 1-9
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